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Complements of unions: Insights on spaceability and applications
IF 0.8 3区 数学
Mathematika Pub Date : 2025-01-08 DOI: 10.1112/mtk.70006
Gustavo Araújo, Anderson Barbosa, Anselmo Baganha Raposo Jr., Geivison Ribeiro
{"title":"Complements of unions: Insights on spaceability and applications","authors":"Gustavo Araújo,&nbsp;Anderson Barbosa,&nbsp;Anselmo Baganha Raposo Jr.,&nbsp;Geivison Ribeiro","doi":"10.1112/mtk.70006","DOIUrl":"https://doi.org/10.1112/mtk.70006","url":null,"abstract":"<p>This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the results of Kitson and Timoney [J. Math. Anal. Appl. <b>378</b> (2011), 680–686]. This criterion extends and recovers some classical results in this theory. The second criterion establishes sufficient conditions for the complement of a union of Lebesgue spaces to be <span></span><math></math>-spaceable, or not, even when they are not locally convex. We use this result to characterize measurable subsets having positive measure. Armed with these results, we have improved existing results in environments such as Lebesgue measurable function sets, spaces of continuous functions, sequence spaces, nowhere Hölder function sets, Sobolev spaces, non-absolutely summing operator spaces and even sets of functions of bounded variation.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113276","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
Diagonal cubic forms and the large sieve
IF 0.8 3区 数学
Mathematika Pub Date : 2025-01-02 DOI: 10.1112/mtk.70008
Victor Y. Wang
{"title":"Diagonal cubic forms and the large sieve","authors":"Victor Y. Wang","doi":"10.1112/mtk.70008","DOIUrl":"https://doi.org/10.1112/mtk.70008","url":null,"abstract":"<p>Let <span></span><math></math> be the number of integral zeros <span></span><math></math> of <span></span><math></math>. Works of Hooley and Heath-Brown imply <span></span><math></math>, if one assumes automorphy and grand Riemann hypothesis for certain Hasse–Weil <span></span><math></math>-functions. Assuming instead a natural large sieve inequality, we recover the same bound on <span></span><math></math>. This is part of a more general statement, for diagonal cubic forms in <span></span><math></math> variables, where we allow approximations to Hasse–Weil <span></span><math></math>-functions.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110845","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
The radial symmetry of minimizers to the weighted Dirichlet energy in
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-28 DOI: 10.1112/mtk.70007
David Kalaj
{"title":"The radial symmetry of minimizers to the weighted Dirichlet energy in","authors":"David Kalaj","doi":"10.1112/mtk.70007","DOIUrl":"https://doi.org/10.1112/mtk.70007","url":null,"abstract":"<p>Let <span></span><math></math> and <span></span><math></math> be annuli in <span></span><math></math>. Let <span></span><math></math>, and assume that <span></span><math></math> is the class of Sobolev <span></span><math></math> homeomorphisms of <span></span><math></math> onto <span></span><math></math>. Then, we consider the following Dirichlet-type energy of <span></span><math></math>:\u0000\u0000 </p><p>For general <span></span><math></math>, we minimize the Dirichlet-type integral <span></span><math></math> throughout the class of radial mappings between given annuli, and this minimum always exists for <span></span><math></math>. For <span></span><math></math>, the image annulus cannot be too thick, which is opposite to the Nitsche-type phenomenon known for the standard Dirichlet energy, where the image annulus cannot be too thin.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120151","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
On the zeros of odd weight Eisenstein series
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-22 DOI: 10.1112/mtk.70004
Jan-Willem van Ittersum, Berend Ringeling
{"title":"On the zeros of odd weight Eisenstein series","authors":"Jan-Willem van Ittersum,&nbsp;Berend Ringeling","doi":"10.1112/mtk.70004","DOIUrl":"https://doi.org/10.1112/mtk.70004","url":null,"abstract":"<p>We count the number of zeros of the holomorphic odd weight Eisenstein series in all <span></span><math></math>-translates of the standard fundamental domain.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118148","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
Lower bounds for the large deviations of Selberg's central limit theorem 塞尔伯格中心极限定理大偏差的下界
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-11 DOI: 10.1112/mtk.70002
Louis-Pierre Arguin, Emma Bailey
{"title":"Lower bounds for the large deviations of Selberg's central limit theorem","authors":"Louis-Pierre Arguin,&nbsp;Emma Bailey","doi":"10.1112/mtk.70002","DOIUrl":"https://doi.org/10.1112/mtk.70002","url":null,"abstract":"<p>Let <span></span><math></math> and <span></span><math></math>. We prove that, for any <span></span><math></math> and <span></span><math></math> as <span></span><math></math>,\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860913","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 family of singular Brascamp–Lieb inequalities with dimension datum (1,2,2,1) 关于维数为（1,2,2,1）的奇异Brascamp-Lieb不等式族
IF 0.8 3区 数学
Mathematika Pub Date : 2024-12-08 DOI: 10.1112/mtk.70003
Fred Yu-Hsiang Lin
{"title":"On the family of singular Brascamp–Lieb inequalities with dimension datum (1,2,2,1)","authors":"Fred Yu-Hsiang Lin","doi":"10.1112/mtk.70003","DOIUrl":"https://doi.org/10.1112/mtk.70003","url":null,"abstract":"<p>Motivated by the triangular Hilbert transform, we classify a certain family of singular Brascamp–Lieb forms which we associate with the dimension datum (1,2,2,1). We determine the exact range of Lebesgue exponents, for which one has singular Brascamp–Lieb inequalities within this family. The remaining observations concern counter examples to boundedness. We compare with a counter-example showing that the triangular Hilbert form does not satisfy singular Brascamp–Lieb bounds in the endpoints.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142860288","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
The index of equidimensional flag manifolds 等维旗流形的指数
IF 0.8 3区 数学
Mathematika Pub Date : 2024-11-20 DOI: 10.1112/mtk.70001
Samik Basu, Bikramjit Kundu
{"title":"The index of equidimensional flag manifolds","authors":"Samik Basu,&nbsp;Bikramjit Kundu","doi":"10.1112/mtk.70001","DOIUrl":"https://doi.org/10.1112/mtk.70001","url":null,"abstract":"<p>In this paper, we consider the flag manifold of <span></span><math></math> orthogonal subspaces of equal dimension that carries an action of the cyclic group of order <span></span><math></math>. We provide a complete calculation of the associated Fadell–Husseini index. This may be thought of as an odd primary version of the computations of Baralić, Blagojevic, Karasev, and Vucic, for the Grassmann manifold <span></span><math></math>. These results have geometric consequences for <span></span><math></math>-fold orthogonal shadows of a convex body.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707822","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
Effective upper bounds on the number of resonances in potential scattering 势散射共振数的有效上限
IF 0.8 3区 数学
Mathematika Pub Date : 2024-11-19 DOI: 10.1112/mtk.70000
Jean-Claude Cuenin
{"title":"Effective upper bounds on the number of resonances in potential scattering","authors":"Jean-Claude Cuenin","doi":"10.1112/mtk.70000","DOIUrl":"https://doi.org/10.1112/mtk.70000","url":null,"abstract":"<p>We prove upper bounds on the number of resonances and eigenvalues of Schrödinger operators <span></span><math></math> with complex-valued potentials, where <span></span><math></math> is odd. The novel feature of our upper bounds is that they are <i>effective</i>, in the sense that they only depend on an exponentially weighted norm of V. Our main focus is on potentials in the Lorentz space <span></span><math></math>, but we also obtain new results for compactly supported or pointwise decaying potentials. The main technical innovation, possibly of independent interest, are singular value estimates for Fourier-extension type operators. The obtained upper bounds not only recover several known results in a unified way, they also provide new bounds for potentials that are not amenable to previous methods.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707960","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 mixed moments of the Riemann zeta function 黎曼兹塔函数的扭曲混合矩
IF 0.8 3区 数学
Mathematika Pub Date : 2024-11-04 DOI: 10.1112/mtk.12284
Javier Pliego
{"title":"Twisted mixed moments of the Riemann zeta function","authors":"Javier Pliego","doi":"10.1112/mtk.12284","DOIUrl":"https://doi.org/10.1112/mtk.12284","url":null,"abstract":"<p>We analyse a collection of twisted mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae comprising on some instances secondary terms of the shape <span></span><math></math> for a suitable constant <span></span><math></math> and a polynomial <span></span><math></math>. Such examinations are performed both unconditionally and under the assumption of a weaker version of the <span></span><math></math>-conjecture.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579670","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
Diophantine approximation by rational numbers of certain parity types 用某些奇偶类型的有理数进行二叉逼近
IF 0.8 3区 数学
Mathematika Pub Date : 2024-10-10 DOI: 10.1112/mtk.12285
Dong Han Kim, Seul Bee Lee, Lingmin Liao
{"title":"Diophantine approximation by rational numbers of certain parity types","authors":"Dong Han Kim,&nbsp;Seul Bee Lee,&nbsp;Lingmin Liao","doi":"10.1112/mtk.12285","DOIUrl":"https://doi.org/10.1112/mtk.12285","url":null,"abstract":"<p>For a given irrational number, we consider the properties of best rational approximations of given parities. There are three different kinds of rational numbers according to the parity of the numerator and denominator, say odd/odd, even/odd, and odd/even rational numbers. We study algorithms to find best approximations by rational numbers of given parities and compare these algorithms with continued fraction expansions.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12285","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142429944","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
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