Mathematische Nachrichten最新文献

{"title":"Sharp convergence rate on Schrödingertype operators","authors":"Meng Wang,&nbsp;Shuijiang Zhao","doi":"10.1002/mana.202400266","DOIUrl":"https://doi.org/10.1002/mana.202400266","url":null,"abstract":"<p>For Schrödinger-type operators in one dimension, we consider the relationship between the convergence rate and the regularity for initial data. By establishing the associated frequency-localized maximal estimates, we prove sharp results up to the endpoints. The optimal range for the wave operator in all dimensions is also obtained.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1082-1096"},"PeriodicalIF":0.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595513","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":"Infinitesimally equivariant bundles on complex manifolds","authors":"Emile Bouaziz","doi":"10.1002/mana.202400284","DOIUrl":"https://doi.org/10.1002/mana.202400284","url":null,"abstract":"<p>We study holomorphic vector bundles equipped with a compatible action of vector field by <i>Lie derivatives</i>. We will show that the dependence of the Lie derivative on a vector field is <i>almost</i> <span></span><math>\u0000 <semantics>\u0000 <mi>O</mi>\u0000 <annotation>$mathcal {O}$</annotation>\u0000 </semantics></math>-linear. More precisely, after an algebraic reformulation, we show that any continuous <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathbf {C}$</annotation>\u0000 </semantics></math>-linear Lie algebra splitting of the symbol map from the Atiyah algebra of a vector bundle on a complex manifold is given by a differential operator, which is further of order at most the rank of the bundle plus one. The proof is quite elementary. When the differential operator we obtain has order 0 we have simply a vector bundle with flat connection, so in a sense, our theorem says that we are always a uniformly bounded order away from this simplest case.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1076-1081"},"PeriodicalIF":0.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595512","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 nonlinear characterization of stochastic completeness of graphs","authors":"Marcel Schmidt,&nbsp;Ian Zimmermann","doi":"10.1002/mana.202400436","DOIUrl":"https://doi.org/10.1002/mana.202400436","url":null,"abstract":"<p>We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem. It is employed to establish a nonlinear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"925-943"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400436","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595342","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":"On the Lyapunov exponents of triangular discrete time-varying systems","authors":"Adam Czornik,&nbsp;Thai Son Doan","doi":"10.1002/mana.202300373","DOIUrl":"https://doi.org/10.1002/mana.202300373","url":null,"abstract":"<p>In this paper, we present upper and lower estimates for the Lyapunov exponents of discrete linear systems with triangular time-varying coefficients. These estimates are expressed by the diagonal elements of the coefficient matrix. As a conclusion from these estimates, we also obtain bounds for the Grobman regularity coefficient.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"976-997"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595337","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":"Rational cohomology of \u0000 \u0000 \u0000 M\u0000 \u0000 4\u0000 ,\u0000 1\u0000 \u0000 \u0000 $mathcal {M}_{4,1}$","authors":"Yiu Man Wong,&nbsp;Angelina Zheng","doi":"10.1002/mana.202400294","DOIUrl":"https://doi.org/10.1002/mana.202400294","url":null,"abstract":"<p>We compute the rational cohomology of the moduli space <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathcal {M}_{4,1}$</annotation>\u0000 </semantics></math> of nonsingular genus 4 curves with one marked point, using Gorinov–Vassiliev's method.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1041-1061"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400294","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595435","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":"Sesquilinear forms as eigenvectors in quasi *-algebras, with an application to ladder elements","authors":"Fabio Bagarello,&nbsp;Hiroshi Inoue,&nbsp;Salvatore Triolo","doi":"10.1002/mana.202400291","DOIUrl":"https://doi.org/10.1002/mana.202400291","url":null,"abstract":"<p>We consider a particular class of sesquilinear forms on a Banach quasi *-algebra <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>A</mi>\u0000 <mo>[</mo>\u0000 <mo>∥</mo>\u0000 <mo>.</mo>\u0000 <mo>∥</mo>\u0000 <mo>]</mo>\u0000 <mo>,</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <msub>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mo>∥</mo>\u0000 <mo>.</mo>\u0000 <mo>∥</mo>\u0000 </mrow>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>]</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$({cal A}[Vert .Vert],{cal A}_0[Vert .Vert _0])$</annotation>\u0000 </semantics></math> that we call <i>eigenstates of an element</i> <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 <mo>∈</mo>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <annotation>$ain {cal A}$</annotation>\u0000 </semantics></math>, and we deduce some of their properties. We further apply our definition to a family of ladder elements, that is, elements of <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>${cal A}$</annotation>\u0000 </semantics></math> obeying certain commutation relations physically motivated, and we discuss several results, including orthogonality and biorthogonality of the forms, via Gelfand–Naimark–Segal (GNS) representation.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1062-1075"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400291","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595341","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":"A sufficient condition for boundedness of maximal operator on weighted generalized Orlicz spaces","authors":"Vertti Hietanen","doi":"10.1002/mana.202400496","DOIUrl":"https://doi.org/10.1002/mana.202400496","url":null,"abstract":"<p>We prove that the Hardy–Littlewood maximal operator is bounded in the weighted generalized Orlicz space if the weight satisfies the classical Muckenhoupt condition <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$A_p$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>→</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>φ</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <msup>\u0000 <mi>t</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$t rightarrow frac{varphi (x,t)}{t^p}$</annotation>\u0000 </semantics></math> is almost increasing in addition to the standard conditions.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"944-954"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595434","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":"Partial Hölder regularity for asymptotically convex functionals with borderline double-phase growth","authors":"Wenrui Chang,&nbsp;Shenzhou Zheng","doi":"10.1002/mana.202400388","DOIUrl":"https://doi.org/10.1002/mana.202400388","url":null,"abstract":"<p>We study partial Hölder regularity of the local minimizers <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>∈</mo>\u0000 <msubsup>\u0000 <mi>W</mi>\u0000 <mi>loc</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>;</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$uin W_{mathrm{loc}}^{1,1}(Omega;{mathbb {R}^N})$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$Nge 1$</annotation>\u0000 </semantics></math> to the integral functional <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>∫</mo>\u0000 <mi>Ω</mi>\u0000 </msub>\u0000 <mi>F</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>D</mi>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mspace></mspace>\u0000 <mi>d</mi>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <annotation>$int _Omega F(x,u,Du),dx$</annotation>\u0000 </semantics></math> in a bounded domain <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Omega subset mathbb {R}^n$</annotation>\u0000 </semantics></math> for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$nge 2$</annotation>\u0000 </semantics></math>. Under the assumption of asymptotically convex to the borderline double-phase functional\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1018-1040"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595338","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 linearization and uniqueness of preduals","authors":"Karsten Kruse","doi":"10.1002/mana.202400355","DOIUrl":"https://doi.org/10.1002/mana.202400355","url":null,"abstract":"&lt;p&gt;We study strong linearizations and the uniqueness of preduals of locally convex Hausdorff spaces of scalar-valued functions. Strong linearizations are special preduals. A locally convex Hausdorff space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {F}(Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of scalar-valued functions on a nonempty set &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;annotation&gt;$Omega$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is said to admit a &lt;i&gt;strong linearization&lt;/i&gt; if there are a locally convex Hausdorff space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;annotation&gt;$Y$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, a map &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$delta: Omega rightarrow Y$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and a topological isomorphism &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$T: mathcal {F}(Omega)rightarrow Y_{b}^{prime }$&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;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;∘&lt;/mo&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$T(f)circ delta = f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for all &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$fin mathcal {F}(Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We give sufficient conditions that allow us to lift strong lin","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"955-975"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400355","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595339","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":"On the spaces dual to combinatorial Banach spaces","authors":"Piotr Borodulin-Nadzieja,&nbsp;Sebastian Jachimek,&nbsp;Anna Pelczar-Barwacz","doi":"10.1002/mana.202300303","DOIUrl":"https://doi.org/10.1002/mana.202300303","url":null,"abstract":"<p>We present quasi-Banach spaces which are closely related to the duals of combinatorial Banach spaces. More precisely, for a compact family <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathcal {F}$</annotation>\u0000 </semantics></math> of finite subsets of <span></span><math>\u0000 <semantics>\u0000 <mi>ω</mi>\u0000 <annotation>$omega$</annotation>\u0000 </semantics></math> we define a quasi-norm <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mrow>\u0000 <mo>∥</mo>\u0000 <mo>·</mo>\u0000 <mo>∥</mo>\u0000 </mrow>\u0000 <mi>F</mi>\u0000 </msup>\u0000 <annotation>$Vert cdot Vert ^mathcal {F}$</annotation>\u0000 </semantics></math> whose Banach envelope is the dual norm for the combinatorial space generated by <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathcal {F}$</annotation>\u0000 </semantics></math>. Such quasi-norms seem to be much easier to handle than the dual norms and yet the quasi-Banach spaces induced by them share many properties with the dual spaces. We show that the quasi-Banach spaces induced by large families (in the sense of Lopez-Abad and Todorcevic) are <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℓ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$ell _1$</annotation>\u0000 </semantics></math>-saturated and do not have the Schur property. In particular, this holds for the Schreier families.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"998-1017"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595340","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}