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On Wiener’s lemma on locally compact Abelian groups 关于局部紧阿贝尔群的Wiener引理
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-10-27 DOI: 10.1007/s00013-025-02188-w
Philippe Jaming, Karim Kellay, Rolando Perez III
{"title":"On Wiener’s lemma on locally compact Abelian groups","authors":"Philippe Jaming,&nbsp;Karim Kellay,&nbsp;Rolando Perez III","doi":"10.1007/s00013-025-02188-w","DOIUrl":"10.1007/s00013-025-02188-w","url":null,"abstract":"<div><p>We establish a general form of Wiener’s lemma for measures on locally compact Abelian groups by using Fourier analysis and the theory of Følner sequences. Our approach provides a unified framework that encompasses both the discrete and continuous cases. We also show a version of Wiener’s lemma for Bochner–Riesz means on both <span>({mathbb {R}}^d)</span> and <span>({mathbb {T}}^d)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"61 - 70"},"PeriodicalIF":0.5,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The Choquard-type Brézis–Nirenberg problem in 4D 4D的choquard型brsamzis - nirenberg问题
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-10-22 DOI: 10.1007/s00013-025-02187-x
Wenjing Chen, Zexi Wang
{"title":"The Choquard-type Brézis–Nirenberg problem in 4D","authors":"Wenjing Chen,&nbsp;Zexi Wang","doi":"10.1007/s00013-025-02187-x","DOIUrl":"10.1007/s00013-025-02187-x","url":null,"abstract":"<div><p>In this paper, we focus on the following Choquard-type Brézis–Nirenberg problem: </p><div><div><span>$$begin{aligned} left{ begin{array}{ll} -Delta u=displaystyle Bigg (int limits _{Omega }frac{u^{4-frac{alpha }{2}}(y)}{|x-y|^alpha }dyBigg )u^{3-frac{alpha }{2}}+varepsilon u, &amp; hbox {in} Omega , u&gt;0, &amp; hbox {in} Omega , u=0, &amp; hbox {on} partial Omega , end{array} right. end{aligned}$$</span></div></div><p>where <span>(Omega )</span> is a smooth bounded domain in <span>(mathbb {R}^4)</span>, <span>(alpha in (0,4))</span>, <span>(4-frac{alpha }{2})</span> is the upper critical exponent in the sense of the Hardy–Littlewood–Sobolev inequality, and <span>(varepsilon &gt;0)</span> is a small parameter. By applying the reduction argument, we prove the existence of solutions, which blow up and concentrate around the critical points of the Robin function as <span>(varepsilon rightarrow 0)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 6","pages":"649 - 658"},"PeriodicalIF":0.5,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145486543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Further generalizations of Girstmair’s irreducibility criterion 关于Girstmair不可约准则的进一步推广
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-10-15 DOI: 10.1007/s00013-025-02184-0
Rishu Garg, Jitender Singh, Sanjeev Kumar
{"title":"Further generalizations of Girstmair’s irreducibility criterion","authors":"Rishu Garg,&nbsp;Jitender Singh,&nbsp;Sanjeev Kumar","doi":"10.1007/s00013-025-02184-0","DOIUrl":"10.1007/s00013-025-02184-0","url":null,"abstract":"<div><p>In this article, some generalizations of Girstmair’s irreducibility criterion have been established for polynomials having integer coefficients. These results for the ring of polynomials over the integers accentuate significant bounds on the number of irreducible factors of the underlying polynomial <i>f</i> apart from irreducibility under some austere factorization and divisibility conditions imposed on the integers <i>f</i>(<i>m</i>) and <span>(f^{(i)}(m))</span>, the <i>i</i>-th formal derivative of <i>f</i> at <i>m</i> strictly superceding the height <span>(H_f)</span> of <i>f</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 6","pages":"589 - 597"},"PeriodicalIF":0.5,"publicationDate":"2025-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145486600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Tensor products of compact quantum metric spaces 紧致量子度量空间的张量积
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-10-10 DOI: 10.1007/s00013-025-02182-2
Botao Long, Ghadir Sadeghi
{"title":"Tensor products of compact quantum metric spaces","authors":"Botao Long,&nbsp;Ghadir Sadeghi","doi":"10.1007/s00013-025-02182-2","DOIUrl":"10.1007/s00013-025-02182-2","url":null,"abstract":"<div><p>A compact quantum metric space is a unital <span>(C^*)</span>-algebra equipped with a Lip-norm. We prove that the (infinite) tensor product of compact quantum metric spaces is a compact quantum metric space for any <span>(C^*)</span>-norm on the algebraic tensor product.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 6","pages":"637 - 647"},"PeriodicalIF":0.5,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145486590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On the minimal generator number of a polycyclic nilpotent-by-finite group 关于多环幂零有限群的最小生成数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-10-07 DOI: 10.1007/s00013-025-02183-1
Bettina Eick
{"title":"On the minimal generator number of a polycyclic nilpotent-by-finite group","authors":"Bettina Eick","doi":"10.1007/s00013-025-02183-1","DOIUrl":"10.1007/s00013-025-02183-1","url":null,"abstract":"<div><p>The determination of the minimal generator number <i>d</i>(<i>G</i>) of a polycyclic group <i>G</i> is one of the few still open problems in the algorithmic theory of these groups. If <span>(hat{G})</span> is the profinite completion of <i>G</i>, then it is known that <span>(d(G) = d(hat{G}))</span> or <span>(d(G) = d(hat{G}) +1)</span> holds. The aim here is to introduce a construction for <span>(d(hat{G}))</span> if <i>G</i> is polycyclic and nilpotent-by-finite.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 6","pages":"569 - 577"},"PeriodicalIF":0.5,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02183-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145486544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Singular minimal surfaces with constant curvature 曲率恒定的奇异极小曲面
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-24 DOI: 10.1007/s00013-025-02181-3
Rafael López
{"title":"Singular minimal surfaces with constant curvature","authors":"Rafael López","doi":"10.1007/s00013-025-02181-3","DOIUrl":"10.1007/s00013-025-02181-3","url":null,"abstract":"<div><p>We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres, and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with constant mean curvature.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 6","pages":"659 - 670"},"PeriodicalIF":0.5,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145486567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The Auslander bound for complexes 澳大利亚人前往建筑群
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-22 DOI: 10.1007/s00013-025-02179-x
Andrew J. Soto Levins
{"title":"The Auslander bound for complexes","authors":"Andrew J. Soto Levins","doi":"10.1007/s00013-025-02179-x","DOIUrl":"10.1007/s00013-025-02179-x","url":null,"abstract":"<div><p>If a module <i>M</i> has finite projective dimension, then the Ext modules of <i>M</i> against any other module eventually vanish and the projective dimension of <i>M</i> gives a uniform bound for this vanishing. For modules of infinite projective dimension, there can still exist a bound. Such a bound is called the Auslander bound. In this paper, we define a similar bound for complexes and give applications.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 1","pages":"29 - 39"},"PeriodicalIF":0.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02179-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145969472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Hadwiger’s conjecture holds for strongly monotypic polytopes 哈德维格猜想对强单型多面体成立
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-15 DOI: 10.1007/s00013-025-02170-6
Vuong Bui
{"title":"Hadwiger’s conjecture holds for strongly monotypic polytopes","authors":"Vuong Bui","doi":"10.1007/s00013-025-02170-6","DOIUrl":"10.1007/s00013-025-02170-6","url":null,"abstract":"<div><p>Hadwiger’s conjecture in combinatorial geometry states that any <i>n</i>-dimensional convex body can be covered by at most <span>(2^n)</span> smaller bodies homothetic to the original body. We prove Hadwiger’s conjecture for strongly monotypic polytopes by studying a characterization of the set of normals. One of the nice properties of (strongly) monotypic polytopes is that the set of normals decides the combinatorics of the polytope.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"561 - 568"},"PeriodicalIF":0.5,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Ma–Qiu index, presentation distance, and local moves in knot theory 结点理论中的马丘指数、表示距离和局部移动
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-11 DOI: 10.1007/s00013-025-02168-0
Tetsuya Ito
{"title":"Ma–Qiu index, presentation distance, and local moves in knot theory","authors":"Tetsuya Ito","doi":"10.1007/s00013-025-02168-0","DOIUrl":"10.1007/s00013-025-02168-0","url":null,"abstract":"<div><p>The Ma–Qiu index of a group is the minimum number of normal generators of the commutator subgroup. We show that the Ma–Qiu index gives a lower bound of the presentation distance of two groups, the minimum number of relator replacements to change one group to the other. Since many local moves in knot theory induce relator replacements in knot groups, this shows that the Ma–Qiu index of knot groups gives a lower bound of the Gordian distance based on various local moves. In particular, this gives a unified and simple proof of the Nakanishi index bounds of various unknotting numbers, including virtual or welded knot cases.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"481 - 489"},"PeriodicalIF":0.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A mixed fibration theorem for Hilbert irreducibility on non-proper varieties 非固有变元上希尔伯特不可约的混合纤化定理
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-10 DOI: 10.1007/s00013-025-02177-z
Cedric Luger
{"title":"A mixed fibration theorem for Hilbert irreducibility on non-proper varieties","authors":"Cedric Luger","doi":"10.1007/s00013-025-02177-z","DOIUrl":"10.1007/s00013-025-02177-z","url":null,"abstract":"<div><p>We prove that the weak Hilbert property ascends along a morphism of varieties over an arbitrary field of characteristic zero, under suitable assumptions.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 6","pages":"621 - 626"},"PeriodicalIF":0.5,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145486578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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