Mathematische Nachrichten最新文献

{"title":"On the controllability of an interior set degenerate Schrödinger equation","authors":"Mohamed Alahyane,&nbsp;Abderrazak Chrifi,&nbsp;Younes Echarroudi","doi":"10.1002/mana.202300252","DOIUrl":"https://doi.org/10.1002/mana.202300252","url":null,"abstract":"<p>In this paper, we are interested on the null controllability property of a linear degenerate Schrödinger equation with a degeneracy occurring on an interior subset of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mtext>that is,</mtext>\u0000 <mspace></mspace>\u0000 <mo>∃</mo>\u0000 <msub>\u0000 <mi>W</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>⊂</mo>\u0000 <mo>⊂</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mtext>such that</mtext>\u0000 <mspace></mspace>\u0000 <mo>∀</mo>\u0000 <mi>x</mi>\u0000 <mo>∈</mo>\u0000 <msub>\u0000 <mi>W</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mi>k</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$(0,1), text{ that is, } exists W_{1}subset subset (0,1), text{ such that } forall xin W_{1}, text{ } k(x)=0$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> stands for the quantum diffusion. More precisely, we are concerned with the null controllability phenomenon using the classical procedure founded on a new Carleman estimate and afterward a newfangled observability inequality.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"644-676"},"PeriodicalIF":0.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397208","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":"An asymptotic mean value property for joint eigenfunctions of \u0000 \u0000 G\u0000 $G$\u0000 -invariant differential operators","authors":"Muna Naik,&nbsp;Rudra P. Sarkar","doi":"10.1002/mana.202400009","DOIUrl":"https://doi.org/10.1002/mana.202400009","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>=</mo>\u0000 <mi>G</mi>\u0000 <mo>/</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$X= G/K$</annotation>\u0000 </semantics></math> be a symmetric space of the noncompact type. In this paper, we characterize joint eigenfunctions of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-invariant differential operators on <span></span><math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> through an asymptotic version of the generalized mean value property.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"636-643"},"PeriodicalIF":0.8,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397159","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":"Strong approximation of special functions of bounded variation functions with prescribed jump direction","authors":"Giuliano Lazzaroni,&nbsp;Piotr Wozniak,&nbsp;Caterina Ida Zeppieri","doi":"10.1002/mana.202300346","DOIUrl":"https://doi.org/10.1002/mana.202300346","url":null,"abstract":"<p>In this note, we show that special functions of bounded variation (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>SBV</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{SBV)}$</annotation>\u0000 </semantics></math> functions with jump normal lying in a prescribed set of directions <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$mathcal {N}$</annotation>\u0000 </semantics></math> can be approximated by sequences of <span></span><math>\u0000 <semantics>\u0000 <mi>SBV</mi>\u0000 <annotation>$mathrm{SBV}$</annotation>\u0000 </semantics></math> functions whose jump set is essentially closed, polyhedral, and preserves the orthogonality to <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$mathcal {N}$</annotation>\u0000 </semantics></math>, moreover the functions are smooth away from their jump set.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"312-327"},"PeriodicalIF":0.8,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300346","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143116715","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":"Interpolation of derivatives and ultradifferentiable regularity","authors":"Armin Rainer,&nbsp;Gerhard Schindl","doi":"10.1002/mana.202300567","DOIUrl":"https://doi.org/10.1002/mana.202300567","url":null,"abstract":"<p>Interpolation inequalities for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <annotation>$C^m$</annotation>\u0000 </semantics></math> functions allow to bound derivatives of intermediate order <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>j</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$0 &lt; j&lt;m$</annotation>\u0000 </semantics></math> by bounds for the derivatives of order 0 and <span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math>. We review various interpolation inequalities for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^p$</annotation>\u0000 </semantics></math>-norms (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>p</mi>\u0000 <mo>≤</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1 le p le infty$</annotation>\u0000 </semantics></math>) in arbitrary finite dimensions. They allow us to study ultradifferentiable regularity by lacunary estimates in a comprehensive way, striving for minimal assumptions on the weights.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"617-635"},"PeriodicalIF":0.8,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300567","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396828","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":"The \u0000 \u0000 \u0000 R\u0000 ∞\u0000 \u0000 $R_infty$\u0000 -property and commensurability for nilpotent groups","authors":"Maarten Lathouwers,&nbsp;Thomas Witdouck","doi":"10.1002/mana.202400154","DOIUrl":"https://doi.org/10.1002/mana.202400154","url":null,"abstract":"<p>For finitely generated torsion-free nilpotent groups, the associated Mal'cev Lie algebra of the group is used frequently when studying the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$R_infty$</annotation>\u0000 </semantics></math>-property. Two such groups have isomorphic Mal'cev Lie algebras if and only if they are abstractly commensurable. We show that the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$R_infty$</annotation>\u0000 </semantics></math>-property is not invariant under abstract commensurability within the class of finitely generated torsion-free nilpotent groups by providing counterexamples within a class of 2-step nilpotent groups associated to edge-weighted graphs. These groups are abstractly commensurable to 2-step nilpotent quotients of right-angled Artin groups.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"602-616"},"PeriodicalIF":0.8,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397074","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":"Three-parameter Triebel–Lizorkin spaces associated with a sum of two flag singular integrals","authors":"Yan Chen,&nbsp;Xiangxing Tao,&nbsp;Taotao Zheng","doi":"10.1002/mana.202400208","DOIUrl":"https://doi.org/10.1002/mana.202400208","url":null,"abstract":"<p>In this paper, the authors establish the three-parameter Triebel–Lizorkin spaces and characterize these spaces as the intersection of two flag Triebel–Lizorkin spaces by applying the discrete Littlewood–Paley–Stein analysis. Moreover, they obtain the boundedness of product singular integral operators on the three-parameter Triebel–Lizorkin spaces.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"581-601"},"PeriodicalIF":0.8,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397164","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":"Entropy numbers and box dimension of polynomials and holomorphic functions","authors":"Daniel Carando,&nbsp;Carlos D'Andrea,&nbsp;Leodan A. Torres,&nbsp;Pablo Turco","doi":"10.1002/mana.202400042","DOIUrl":"https://doi.org/10.1002/mana.202400042","url":null,"abstract":"<p>We study entropy numbers and box dimension of (the image of) homogeneous polynomials and holomorphic functions between Banach spaces. First, we see that entropy numbers and box dimensions of subsets of Banach spaces are related. We show that the box dimension of the image of a ball under a homogeneous polynomial is finite if and only if it spans a finite-dimensional subspace, but this is not true for holomorphic functions. Furthermore, we relate the entropy numbers of a holomorphic function to those of the polynomials of its Taylor series expansion. As a consequence, if the box dimension of the image of a ball by a holomorphic function <span></span><math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> is finite, then the entropy numbers of the polynomials in the Taylor series expansion of <span></span><math>\u0000 <semantics>\u0000 <mi>f</mi>\u0000 <annotation>$f$</annotation>\u0000 </semantics></math> at any point of the ball belong to <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℓ</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$ell _p$</annotation>\u0000 </semantics></math> for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$p&gt;1$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"567-580"},"PeriodicalIF":0.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397165","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":"Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous","authors":"Lorenzo Dello Schiavo,&nbsp;Ronan Herry,&nbsp;Eva Kopfer,&nbsp;Karl-Theodor Sturm","doi":"10.1002/mana.202400169","DOIUrl":"https://doi.org/10.1002/mana.202400169","url":null,"abstract":"<p>For an arbitrary dimension <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>, we study: \u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"244-281"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400169","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120096","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":"Twisted conjugacy in soluble arithmetic groups","authors":"Paula M. Lins de Araujo,&nbsp;Yuri Santos Rego","doi":"10.1002/mana.202300448","DOIUrl":"https://doi.org/10.1002/mana.202300448","url":null,"abstract":"<p>Reidemeister numbers of group automorphisms encode the number of twisted conjugacy classes of groups and might yield information about self-maps of spaces related to the given objects. Here, we address a question posed by Gonçalves and Wong in the mid-2000s: we construct an infinite series of compact connected solvmanifolds (that are <i>not</i> <i>nil</i>manifolds) of strictly increasing dimensions and all of whose self-homotopy equivalences have vanishing Nielsen number. To this end, we establish a sufficient condition for a prominent (infinite) family of soluble linear groups to have the so-called property <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$R_infty$</annotation>\u0000 </semantics></math>. In particular, we generalize or complement earlier results due to Dekimpe, Gonçalves, Kochloukova, Nasybullov, Taback, Tertooy, Van den Bussche, and Wong, showing that many soluble <span></span><math>\u0000 <semantics>\u0000 <mi>S</mi>\u0000 <annotation>$S$</annotation>\u0000 </semantics></math>-arithmetic groups have <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$R_infty$</annotation>\u0000 </semantics></math> and suggesting a conjecture in this direction.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"763-793"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300448","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595679","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":"Abstract integro-differential equations with state-dependent integration intervals: Existence, uniqueness, and local well-posedness","authors":"Eduardo Hernandez,&nbsp;Shashank Pandey,&nbsp;Dwijendra N. Pandey","doi":"10.1002/mana.202400126","DOIUrl":"https://doi.org/10.1002/mana.202400126","url":null,"abstract":"<p>In this work, we study a new class of integro-differential equations with delay, where the informations from the past are represented as an average of the state over state-dependent integration intervals. We establish results on the local and global existence and qualitative properties of solutions. The models presented and the ideas developed will allow the generalization of an extensive literature on different classes of functional differential equations. The last section presents some examples motivated by integro-differential equations arising in the theory of population dynamics.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"356-384"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120066","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}