Mathematische Nachrichten最新文献

{"title":"Local \u0000 \u0000 H\u0000 $H$\u0000 -principles for holomorphic partial differential relations","authors":"Luis Giraldo,&nbsp;Guillermo Sánchez-Arellano","doi":"10.1002/mana.202300492","DOIUrl":"https://doi.org/10.1002/mana.202300492","url":null,"abstract":"<p>We introduce the notion of the realifications of an arbitrary <i>holomorphic partial differential relation</i> <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$mathcal {R}$</annotation>\u0000 </semantics></math>, that are partial differential relations associated with the restrictions of <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$mathcal {R}$</annotation>\u0000 </semantics></math> to totally real submanifolds of maximal dimension. Our main result states that if any realification of an open holomorphic partial differential relation over a Stein manifold satisfies a relative to domain <span></span><math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-principle, then it is possible to deform any formal solution into one that is holonomic in a neighborhood of a Lagrangian skeleton of the Stein manifold. If the Stein manifold is an open Riemann surface or it has finite type, then that skeleton is independent of the formal solution. This yields the existence of local <span></span><math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-principles over that skeleton. These results broaden those obtained by Forstnerič and Slapar on holomorphic immersions, submersions, and complex contact structures for instance to holomorphic local <span></span><math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-principles for the corresponding version in the complex category of some other classical examples of distributions and structures in the smooth category such as complex even contact, complex Engel, and complex twisted locally conformal symplectic structures.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1521-1548"},"PeriodicalIF":0.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reducibility of ultra-differentiable quasi-periodic linear systems","authors":"Xiangyuan Zhang,&nbsp;Dongfeng Zhang","doi":"10.1002/mana.202300122","DOIUrl":"https://doi.org/10.1002/mana.202300122","url":null,"abstract":"&lt;p&gt;In ultra-differentiable classes, this paper studies the reducibility of the quasi-periodic linear system &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;̇&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$dot{x}=(A+varepsilon Q(t))x,xin mathbb {R}^{d}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$A$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a constant matrix with different eigenvalues &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mtext&gt;…&lt;/mtext&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$lambda =(lambda _{1},lambda _{2},ldots,lambda _{d})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Q(t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a ultra-differentiable quasi-periodic matrix with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; basic frequencies &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1482-1495"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Cauchy problem of three-dimensional compressible magneto-micropolar fluids with vacuum","authors":"Mingyu Zhang","doi":"10.1002/mana.202400144","DOIUrl":"https://doi.org/10.1002/mana.202400144","url":null,"abstract":"<p>In this paper, we study the Cauchy problem of three-dimensional compressible magneto-micropolar fluids. Applying the energy method and the structural characteristics of the model, the global existence and uniqueness of classical solutions are established provided that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>∥</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <msub>\u0000 <mo>∥</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$Vert mathbf { B}_0Vert _{L^3}+M_0$</annotation>\u0000 </semantics></math> is suitable small, where <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathbf { B}_0$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$M_0$</annotation>\u0000 </semantics></math> represent the initial magnetic field and upper bound of initial density. It is worth mentioning that both the vacuum states of initial density and the possible random largeness of initial energy are allowed. Thus, the results obtained particularly extend the one due to Wei et al., where the global well-posedness of smooth solutions with small perturbations of initial data was proved.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1449-1481"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds","authors":"Isolda Cardoso,&nbsp;Ana Cosgaya,&nbsp;Silvio Reggiani","doi":"10.1002/mana.202400213","DOIUrl":"https://doi.org/10.1002/mana.202400213","url":null,"abstract":"<p>A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for 6-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable of triangular type. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1496-1520"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterizations of the Sobolev space H1 on the boundary of a strongly Lipschitz domain in 3-D","authors":"Nathanael Skrepek","doi":"10.1002/mana.202400282","DOIUrl":"https://doi.org/10.1002/mana.202400282","url":null,"abstract":"<p>In this work, we investigate the Sobolev space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>∂</mi>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{H}^{1}(partial Omega)$</annotation>\u0000 </semantics></math> on a strongly Lipschitz boundary <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>Ω</mi>\u0000 </mrow>\u0000 <annotation>$partial Omega$</annotation>\u0000 </semantics></math>, that is, <span></span><math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math> is a strongly Lipschitz domain (not necessarily bounded). In most of the literature, this space is defined via charts and Sobolev spaces on flat domains. We show that there is a different approach via differential operators on <span></span><math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math> and a weak formulation directly on the boundary that leads to the same space. This second characterization of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>∂</mi>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{H}^{1}(partial Omega)$</annotation>\u0000 </semantics></math> is in particular of advantage, when it comes to traces of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 <mo>(</mo>\u0000 <mo>curl</mo>\u0000 <mo>,</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{H}(operatorname{curl},Omega)$</annotation>\u0000 </semantics></math> vector fields.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1342-1355"},"PeriodicalIF":0.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400282","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonstandard representation of the Dirichlet form and application to the comparison theorem","authors":"Haosui Duanmu,&nbsp;Aaron Smith","doi":"10.1002/mana.202300246","DOIUrl":"https://doi.org/10.1002/mana.202300246","url":null,"abstract":"<p>The Dirichlet form is a generalization of the Laplacian, heavily used in the study of many diffusion-like processes. In this paper, we present a <i>nonstandard representation theorem</i> for the Dirichlet form, showing that the usual Dirichlet form can be well-approximated by a <i>hyperfinite</i> sum. One of the main motivations for such a result is to provide a tool for directly translating results about Dirichlet forms on finite or countable state spaces to results on more general state spaces, without having to translate the details of the proofs. As an application, we compare the Dirichlet forms of two general Markov processes by applying the transfer of the well-known comparison theorem for finite Markov processes.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1167-1183"},"PeriodicalIF":0.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300246","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"M\u0000 $M$\u0000 -Ideals in real operator algebras","authors":"David P. Blecher,&nbsp;Matthew Neal,&nbsp;Antonio M. Peralta,&nbsp;Shanshan Su","doi":"10.1002/mana.202400227","DOIUrl":"https://doi.org/10.1002/mana.202400227","url":null,"abstract":"<p>In a recent paper, we showed that a subspace of a real <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>JBW</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm JBW}^*$</annotation>\u0000 </semantics></math>-triple is an <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>-summand if and only if it is a <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>weak</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm weak}^*$</annotation>\u0000 </semantics></math>-closed triple ideal. As a consequence, <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>-ideals of real <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>JB</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm JB}^*$</annotation>\u0000 </semantics></math>-triples, including real <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm C}^*$</annotation>\u0000 </semantics></math>-algebras, real <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>JB</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${rm JB}^*$</annotation>\u0000 </semantics></math>-algebras and real TROs, correspond to norm-closed triple ideals. In this paper, we extend this result by identifying the <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>-ideals in (possibly non-self-adjoint) real operator algebras and Jordan operator algebras. The argument for this is necessarily different. We also give simple characterizations of one-sided <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>-ideals in real operator algebras, and give some applications to that theory.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1328-1341"},"PeriodicalIF":0.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A characterization of some finite simple groups by their character codegrees","authors":"Hung P. Tong-Viet","doi":"10.1002/mana.202400283","DOIUrl":"https://doi.org/10.1002/mana.202400283","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a finite group and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;annotation&gt;$chi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a complex irreducible character of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The codegree of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;annotation&gt;$chi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is defined by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;cod&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;ker&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$textrm {cod}(chi)=|G:textrm {ker}(chi)|/chi (1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ker&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$textrm {ker}(chi)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the kernel of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;annotation&gt;$chi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In this paper, we show that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a finite simple exceptional group of Lie type or a finite simple projective special linear group and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is any finite group such that the character codegree sets of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; coincide, then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;ann","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1356-1369"},"PeriodicalIF":0.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400283","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hodge loci associated with linear subspaces intersecting in codimension one","authors":"Remke Kloosterman","doi":"10.1002/mana.202400066","DOIUrl":"https://doi.org/10.1002/mana.202400066","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Xsubset mathbf {P}^{2k+1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a smooth hypersurface containing two &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional linear spaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Pi _1,Pi _2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;dim&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;∩&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$dim Pi _1cap Pi _2=k-1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In this paper, we study the question whether the Hodge loci &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;NL&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Π&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{NL}([Pi _1]+lambda [Pi _2])$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1220-1229"},"PeriodicalIF":0.8,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400066","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variable Hardy spaces on spaces of homogeneous type and applications to variable Hardy spaces associated with elliptic operators having Robin boundary conditions on Lipschitz domains","authors":"Xiong Liu,&nbsp;Wenhua Wang","doi":"10.1002/mana.202400300","DOIUrl":"https://doi.org/10.1002/mana.202400300","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(mathcal {X},d,mu)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a space of homogeneous type with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mu (mathcal {X})&lt;infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$p(cdot):mathcal {X}rightarrow (0,infty)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; a variable exponent function satisfying &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0&lt;p_-&lt;infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;ess&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;inf&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$p_-:=mathrm{ess inf}_{xin mathcal {X}}p(x)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Assume that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$L$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a nonnegative self-adjoint operator on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1370-1440"},"PeriodicalIF":0.8,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}