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Expositiones Mathematicae最新文献

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Geometric characterization of Ahlfors regular spaces in terms of dyadic cubes related to wavelets with its applications to equivalences of Lipschitz spaces 用与小波相关的二元立方体描述阿赫福斯规则空间的几何特征，并将其应用于等价利普齐兹空间
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-05-13 DOI: 10.1016/j.exmath.2024.125574
Fan Wang , Dachun Yang , Wen Yuan
{"title":"Geometric characterization of Ahlfors regular spaces in terms of dyadic cubes related to wavelets with its applications to equivalences of Lipschitz spaces","authors":"Fan Wang ,&nbsp;Dachun Yang ,&nbsp;Wen Yuan","doi":"10.1016/j.exmath.2024.125574","DOIUrl":"10.1016/j.exmath.2024.125574","url":null,"abstract":"<div><p>Assume that <span><math><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>μ</mi><mo>)</mo></mrow></math></span> is a space of homogeneous type introduced by R. R. Coifman and G. Weiss. In this article, the authors establish a geometric characterization of Ahlfors regular spaces via the dyadic cubes constructed by T. Hytönen and A. Kairema. As applications, the authors show that Lipschitz spaces defined via the quasi-metric under consideration and Lipschitz spaces defined via the measure under consideration coincide with equivalent norms if and only if <span><math><mi>X</mi></math></span> is an Ahlfors regular space. Moreover, the authors also prove that Lipschitz spaces defined via the quasi-metric under consideration and Campanato spaces defined via balls coincide with equivalent norms if and only if <span><math><mi>X</mi></math></span> is an Ahlfors regular space.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141040800","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
Kernel-algorithms in frame-approximations 框架逼近中的核算法
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-05-01 DOI: 10.1016/j.exmath.2024.125583
P. Jorgensen, Myung-Sin Song, James Tian
{"title":"Kernel-algorithms in frame-approximations","authors":"P. Jorgensen, Myung-Sin Song, James Tian","doi":"10.1016/j.exmath.2024.125583","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125583","url":null,"abstract":"","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141134319","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 short review of finite approximations and unconventional physics 有限近似和非常规物理学简评
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-05-01 DOI: 10.1016/j.exmath.2024.125573
Trond Digernes
{"title":"A short review of finite approximations and unconventional physics","authors":"Trond Digernes","doi":"10.1016/j.exmath.2024.125573","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125573","url":null,"abstract":"","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141052781","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
Periodicity of general multidimensional continued fractions using repetend matrix form 使用重复矩阵形式的一般多维续分数的周期性
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-04-04 DOI: 10.1016/j.exmath.2024.125571
Hanka Řada , Štěpán Starosta , Vítězslav Kala
{"title":"Periodicity of general multidimensional continued fractions using repetend matrix form","authors":"Hanka Řada ,&nbsp;Štěpán Starosta ,&nbsp;Vítězslav Kala","doi":"10.1016/j.exmath.2024.125571","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125571","url":null,"abstract":"<div><p>We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend and use it to prove that a number of vectors have an eventually periodic expansion in the Algebraic Jacobi–Perron algorithm. Further, we give criteria for vectors to have purely periodic expansions; in particular, the vector cannot be totally positive.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140554317","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 variation on von Neumann Entropy and a result of Varadarajan 冯-诺依曼熵的变体和瓦拉达拉詹的一个结果
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-04-01 DOI: 10.1016/j.exmath.2024.125572
Glenn D. Appleby
{"title":"A variation on von Neumann Entropy and a result of Varadarajan","authors":"Glenn D. Appleby","doi":"10.1016/j.exmath.2024.125572","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125572","url":null,"abstract":"","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140796018","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 note on the base-p expansions of putative counterexamples to the p-adic Littlewood conjecture 关于 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e27" altimg="si13.svg" 假设反例的基点展开的说明
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-03-20 DOI: 10.1016/j.exmath.2024.125548
J. Blackman , S. Kristensen , M.J. Northey
{"title":"A note on the base-p expansions of putative counterexamples to the p-adic Littlewood conjecture","authors":"J. Blackman ,&nbsp;S. Kristensen ,&nbsp;M.J. Northey","doi":"10.1016/j.exmath.2024.125548","DOIUrl":"10.1016/j.exmath.2024.125548","url":null,"abstract":"<div><p>In this paper, we investigate the base-<span><math><mi>p</mi></math></span> expansions of putative counterexamples to the <span><math><mi>p</mi></math></span>-adic Littlewood conjecture of de Mathan and Teulié. We show that if a counterexample exists, then so does a counterexample whose base-<span><math><mi>p</mi></math></span> expansion is uniformly recurrent. Furthermore, we show that if the base-<span><math><mi>p</mi></math></span> expansion of <span><math><mi>x</mi></math></span> is a morphic word <span><math><mrow><mi>τ</mi><mrow><mo>(</mo><msup><mrow><mi>φ</mi></mrow><mrow><mi>ω</mi></mrow></msup><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> where <span><math><mrow><msup><mrow><mi>φ</mi></mrow><mrow><mi>ω</mi></mrow></msup><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></mrow></math></span> contains a subword of the form <span><math><mrow><mi>u</mi><mi>X</mi><mi>u</mi><mi>X</mi><mi>u</mi></mrow></math></span> with <span><math><mrow><msub><mrow><mo>lim</mo></mrow><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></msub><mrow><mo>|</mo><msup><mrow><mi>φ</mi></mrow><mrow><mi>n</mi></mrow></msup><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>|</mo></mrow><mo>=</mo><mi>∞</mi></mrow></math></span>, then <span><math><mi>x</mi></math></span> satisfies the <span><math><mi>p</mi></math></span>-adic Littlewood conjecture. In the special case when <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span>, we show that the conjecture holds for all pure morphic words.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S072308692400015X/pdfft?md5=9882f79608644e821115bc0ed83923d6&pid=1-s2.0-S072308692400015X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140281675","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
Abstract embeddability ranks 抽象可嵌入性等级
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-03-18 DOI: 10.1016/j.exmath.2024.125563
Florent P. Baudier , Christian Rosendal
{"title":"Abstract embeddability ranks","authors":"Florent P. Baudier ,&nbsp;Christian Rosendal","doi":"10.1016/j.exmath.2024.125563","DOIUrl":"10.1016/j.exmath.2024.125563","url":null,"abstract":"<div><p>We describe several ordinal indices that are capable of detecting, according to various metric notions of faithfulness, the embeddability between pairs of Polish spaces. These embeddability ranks are of theoretical interest but seem difficult to estimate in practice. Embeddability ranks, which are easier to estimate in practice, are embeddability ranks generated by Schauder bases. These embeddability ranks are inspired by the nonlinear indices à la Bourgain. In particular, we resolve a problem raised by F. Baudier, G. Lancien, P. Motakis, and Th. Schlumprecht in Coarse and Lipschitz universality, Fund. Math. 254 (2021), no. 2, 181–214, regarding the necessity of additional set-theoretic axioms regarding the main coarse universality result there.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140182011","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 simple proof of the Wiener–Ikehara Tauberian Theorem 维纳-池原陶伯定理的简单证明
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-03-18 DOI: 10.1016/j.exmath.2024.125570
M. Ram Murty , Jagannath Sahoo , Akshaa Vatwani
{"title":"A simple proof of the Wiener–Ikehara Tauberian Theorem","authors":"M. Ram Murty ,&nbsp;Jagannath Sahoo ,&nbsp;Akshaa Vatwani","doi":"10.1016/j.exmath.2024.125570","DOIUrl":"10.1016/j.exmath.2024.125570","url":null,"abstract":"<div><p>The Wiener–Ikehara Tauberian theorem is an important theorem giving an asymptotic formula for the sum of coefficients of a Dirichlet series <span><math><mrow><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>∞</mi></mrow></msubsup><mfrac><mrow><mi>a</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow><mrow><msup><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msup></mrow></mfrac></mrow></math></span>. We provide a simple and elegant proof of the Wiener–Ikehara Tauberian theorem which relies only on basic Fourier analysis and known estimates for the given Dirichlet series. This method also allows us to derive a version of the Wiener–Ikehara theorem with an error term.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140181844","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
Obituary: Bent Fuglede (1925–2023) 讣告本特-福格勒德（1925-2023）
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-03-01 DOI: 10.1016/j.exmath.2023.125531
Liming Ge (Managing Editor)
{"title":"Obituary: Bent Fuglede (1925–2023)","authors":"Liming Ge (Managing Editor)","doi":"10.1016/j.exmath.2023.125531","DOIUrl":"10.1016/j.exmath.2023.125531","url":null,"abstract":"","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S072308692300107X/pdfft?md5=aa8f8838bfe5d66a791a9333d3459373&pid=1-s2.0-S072308692300107X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139409818","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
Geometric criteria for the existence of capillary surfaces in tubes 管道中存在毛细管表面的几何标准
IF 0.7 4区 数学
Expositiones Mathematicae Pub Date : 2024-02-28 DOI: 10.1016/j.exmath.2024.125547
Giorgio Saracco
{"title":"Geometric criteria for the existence of capillary surfaces in tubes","authors":"Giorgio Saracco","doi":"10.1016/j.exmath.2024.125547","DOIUrl":"https://doi.org/10.1016/j.exmath.2024.125547","url":null,"abstract":"<div><p>We review some geometric criteria and prove a refined version, that yield existence of capillary surfaces in tubes <span><math><mrow><mi>Ω</mi><mo>×</mo><mi>R</mi></mrow></math></span> in a gravity free environment, in the case of physical interest, that is, for bounded, open, and simply connected <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>. These criteria rely on suitable weak one-sided bounds on the curvature of the boundary of the cross-section <span><math><mi>Ω</mi></math></span>.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000148/pdfft?md5=8d050c0fb8ec6bbd1f9d3483b6085e70&pid=1-s2.0-S0723086924000148-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140031119","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
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