Mathematische Nachrichten最新文献_第7页

Heat kernel gradient estimates for the Vicsek set Vicsek集的热核梯度估计

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-10-03 DOI: 10.1002/mana.202400180

Fabrice Baudoin, Li Chen

引用次数: 0

Dunkl convolution and elliptic regularity for Dunkl operators Dunkl算子的Dunkl卷积和椭圆正则性

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-27 DOI: 10.1002/mana.202300370

Dominik Brennecken

{"title":"Dunkl convolution and elliptic regularity for Dunkl operators","authors":"Dominik Brennecken","doi":"10.1002/mana.202300370","DOIUrl":"https://doi.org/10.1002/mana.202300370","url":null,"abstract":"We discuss in which cases the Dunkl convolution <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <msub>\u0000 <mo>∗</mo>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 <annotation>$u*_kv$</annotation>\u0000 </semantics></math> of distributions <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 </mrow>\u0000 <annotation>$u,v$</annotation>\u0000 </semantics></math>, possibly both with non-compact support, can be defined and study its analytic properties. We prove results on the (singular-)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called elliptic Dunkl operators. Finally, for the root system <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$A_{n-1}$</annotation>\u0000 </semantics></math> we consider the Riesz distributions <math>\u0000 <semantics>\u0000 <msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>α</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>∈</mo>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$(R_alpha)_{alpha in mathbb {C}}$</annotation>\u0000 </semantics></math> and prove that their Dunkl convolution exists and that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>α</mi>\u0000 </msub>\u0000 <msub>\u0000 <mo>∗</mo>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>β</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>+</mo>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$R_alpha *_kR_beta = R_{alpha +b","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4416-4436"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300370","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862193","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}

引用次数: 0

On the real spectrum of differential operators with PT-symmetric periodic matrix coefficients 具有pt对称周期矩阵系数的微分算子的实谱

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-27 DOI: 10.1002/mana.202300558

Oktay A. Veliev

{"title":"On the real spectrum of differential operators with PT-symmetric periodic matrix coefficients","authors":"Oktay A. Veliev","doi":"10.1002/mana.202300558","DOIUrl":"https://doi.org/10.1002/mana.202300558","url":null,"abstract":"We study the spectrum of the operator <math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> generated by the differential expression of order <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>></mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$n&gt;2$</annotation>\u0000 </semantics></math> with the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>×</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$mtimes m$</annotation>\u0000 </semantics></math> Parity-Time (PT)-symmetric periodic matrix coefficients. The case when <math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> are the odd numbers was investigated in [18]. In this paper, we consider the all remained cases: (a) <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> is an odd number and <math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> is an even number, (b) <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> is an even number and <math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> is an arbitrary positive integer. We find conditions on the coefficients under which in the cases (a) and (b) the spectrum of <math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> contains the sets <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mi>∞</mi>\u0000 <mo>,</mo>\u0000 <mo>−</mo>\u0000 <mi>H</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$(-infty,-H]$</annotation>\u0000 </semantics></math> <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>∪</mo>\u0000 <mo>[</mo>\u0000 <mi>H</mi>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$cup [H,infty)$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[<","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4437-4449"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862194","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}

引用次数: 0

Equivariant birational types and derived categories 等变双向类型和派生类

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-26 DOI: 10.1002/mana.202400006

Christian Böhning, Hans-Christian Graf von Bothmer, Yuri Tschinkel

引用次数: 0

On locally finite groups whose derived subgroup is locally nilpotent 关于导出子群为局部零势的局部有限群

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-26 DOI: 10.1002/mana.202400263

Marco Trombetti

{"title":"On locally finite groups whose derived subgroup is locally nilpotent","authors":"Marco Trombetti","doi":"10.1002/mana.202400263","DOIUrl":"https://doi.org/10.1002/mana.202400263","url":null,"abstract":"A celebrated theorem of Helmut Wielandt shows that the nilpotent residual of the subgroup generated by two subnormal subgroups of a finite group is the subgroup generated by the nilpotent residuals of the subgroups. This result has been extended to saturated formations in Ballester-Bolinches, Ezquerro, and Pedreza-Aguilera [Math. Nachr. 239–240 (2002), 5–10]. Although Wielandt's result is not true in arbitrary locally finite groups, we are able to extend it (even in a stronger form) to homomorphic images of periodic linear groups. Also, all results in Ballester-Bolinches, Ezquerro, and Pedreza-Aguilera [Math. Nachr. 239–240 (2002), 5–10] are extended to locally finite groups, so it is possible to characterize the class of locally finite groups with a locally nilpotent derived subgroup as the largest subgroup-closed saturated formation <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$mathfrak {X}$</annotation>\u0000 </semantics></math> such that, for all <math>\u0000 <semantics>\u0000 <mi>SL</mi>\u0000 <annotation>$mathbf {SL}$</annotation>\u0000 </semantics></math>-closed saturated formations <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathfrak {F}$</annotation>\u0000 </semantics></math>, the <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathfrak {F}$</annotation>\u0000 </semantics></math>-residual of an <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$mathfrak {X}$</annotation>\u0000 </semantics></math>-group generated by <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathfrak {F}$</annotation>\u0000 </semantics></math>-subnormal subgroups is the subgroup generated by their <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathfrak {F}$</annotation>\u0000 </semantics></math>-residuals. Our proofs are based on a reduction theorem that is of an independent interest. Furthermore, we provide strengthened versions of Wielandt's result for other relevant classes of groups, among which we mention the class of paranilpotent groups. A brief discussion on the permutability of the residuals is given at the end of the paper.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 12","pages":"4389-4400"},"PeriodicalIF":0.8,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400263","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142862252","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}

引用次数: 0

Well-posedness of the two-dimensional stationary Navier–Stokes equations around a uniform flow 围绕均匀流动的二维平稳Navier-Stokes方程的适定性

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-26 DOI: 10.1002/mana.202400011

Mikihiro Fujii, Hiroyuki Tsurumi

引用次数: 0

There is no 290-Theorem for higher degree forms 高阶形式没有 290定理

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-24 DOI: 10.1002/mana.202400253

Vítězslav Kala, Om Prakash

引用次数: 0

Note on intrinsic metrics on graphs 关于图表内在指标的说明

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-18 DOI: 10.1002/mana.202400099

Daniel Lenz, Marcel Schmidt, Felix Seifert

引用次数: 0

Nonconcentration phenomenon for one-dimensional reaction–diffusion systems with mass dissipation 具有质量耗散的一维反应扩散系统的非集中现象

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-16 DOI: 10.1002/mana.202300442

Juan Yang, Anna Kostianko, Chunyou Sun, Bao Quoc Tang, Sergey Zelik

{"title":"Nonconcentration phenomenon for one-dimensional reaction–diffusion systems with mass dissipation","authors":"Juan Yang, Anna Kostianko, Chunyou Sun, Bao Quoc Tang, Sergey Zelik","doi":"10.1002/mana.202300442","DOIUrl":"https://doi.org/10.1002/mana.202300442","url":null,"abstract":"Reaction–diffusion systems with mass dissipation are known to possess blow-up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension 1, it has been shown recently that one can have global existence of bounded solutions if nonlinearities are at most cubic. For the cubic intermediate sum condition, that is, nonlinearities might have arbitrarily high growth rates, an additional entropy inequality had to be imposed. In this paper, we remove this extra entropy assumption completely and obtain global boundedness for reaction–diffusion systems with cubic intermediate sum condition. The novel idea is to show a nonconcentration phenomenon for mass dissipating systems, that is the mass dissipation implies a dissipation in a Morrey space <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathsf {M}^{1,delta }(Omega)$</annotation>\u0000 </semantics></math> for some <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$delta &gt;0$</annotation>\u0000 </semantics></math>. As far as we are concerned, it is the first time such a bound is derived for mass dissipating reaction–diffusion systems. The results are then applied to obtain global existence and boundedness of solutions to an oscillatory Belousov–Zhabotinsky system, which satisfies cubic intermediate sum condition but does not fulfill the entropy assumption. Extensions include global existence mass controlled systems with slightly super cubic intermediate sum condition.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4288-4306"},"PeriodicalIF":0.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300442","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642113","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}

引用次数: 0

Twisted Kähler–Einstein metrics on flag varieties 旗变体上的扭曲凯勒-爱因斯坦度量

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-12 DOI: 10.1002/mana.202300553

Eder M. Correa, Lino Grama

{"title":"Twisted Kähler–Einstein metrics on flag varieties","authors":"Eder M. Correa, Lino Grama","doi":"10.1002/mana.202300553","DOIUrl":"10.1002/mana.202300553","url":null,"abstract":"In this paper, we present a description of invariant twisted Kähler–Einstein (tKE) metrics on flag varieties. Additionally, we delve into the applications of the concepts utilized in proving our main result, particularly concerning the existence of the invariant twisted constant scalar curvature Kähler metrics. Moreover, we provide a precise description of the greatest Ricci lower bound for arbitrary Kähler classes on flag varieties. From this description, we establish a sequence of inequalities linked to optimal upper bounds for the volume of Kähler metrics, relying solely on tools derived from the Lie theory. Further, we illustrate our main results through various examples, encompassing full flag varieties, the projectivization of the tangent bundle of <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>${mathbb {P}}^{n+1}$</annotation>\u0000 </semantics></math>, and families of flag varieties with a Picard number 2.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4273-4287"},"PeriodicalIF":0.8,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252029","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}

引用次数: 0