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{"title":"Supercongruences arising from a 7 F 6 hypergeometric transformation formula","authors":"Chen Wang","doi":"10.1515/forum-2023-0239","DOIUrl":"https://doi.org/10.1515/forum-2023-0239","url":null,"abstract":"Using a <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mmultiscripts> <m:mi>F</m:mi> <m:mn>6</m:mn> <m:none /> <m:mprescripts /> <m:mn>7</m:mn> <m:none /> </m:mmultiscripts> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0239_eq_0198.png\" /> <jats:tex-math>{{}_{7}F_{6}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> hypergeometric transformation formula, we prove two supercongruences. In particular, one of these supercongruences confirms a recent conjecture of Guo, Liu and Schlosser, and gives an extension of a supercongruence of Long and Ramakrishna.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"180 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422925","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":"Topological embeddings into transformation monoids","authors":"Serhii Bardyla, Luke Elliott, James D. Mitchell, Yann Péresse","doi":"10.1515/forum-2023-0230","DOIUrl":"https://doi.org/10.1515/forum-2023-0230","url":null,"abstract":"In this paper we consider the questions of which topological semigroups embed topologically into the full transformation monoid &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msup&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;/m:msup&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0230_eq_0294.png\" /&gt; &lt;jats:tex-math&gt;{mathbb{N}^{mathbb{N}}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; or the symmetric inverse monoid &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msub&gt; &lt;m:mi&gt;I&lt;/m:mi&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;/m:msub&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0230_eq_0187.png\" /&gt; &lt;jats:tex-math&gt;{I_{mathbb{N}}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; with their respective canonical Polish semigroup topologies. We characterise those topological semigroups that embed topologically into &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msup&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;/m:msup&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0230_eq_0294.png\" /&gt; &lt;jats:tex-math&gt;{mathbb{N}^{mathbb{N}}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; and belong to any of the following classes: commutative semigroups, compact semigroups, groups, and certain Clifford semigroups. We prove analogous characterisations for topological inverse semigroups and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msub&gt; &lt;m:mi&gt;I&lt;/m:mi&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;/m:msub&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0230_eq_0187.png\" /&gt; &lt;jats:tex-math&gt;{I_{mathbb{N}}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. We construct several examples of countable Polish topological semigroups that do not embed into &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msup&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;/m:msup&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0230_eq_0294.png\" /&gt; &lt;jats:tex-math&gt;{mathbb{N}^{mathbb{N}}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, which answer, in the negative, a recent open problem of Elliott et al. Additionally, we obtain two sufficient conditions for a topological Clifford semigroup to be metrizable, and prove that inversion is automatically continuous in every Clifford subsemigroup of &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msup&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;m:mi&gt;ℕ&lt;/m:mi&gt; &lt;/m:msup&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0230_eq_0294.png\" /&gt; &lt;jats:tex-math&gt;{mathb","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"36 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139374731","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":"Wells-type exact sequence and crossed extensions of algebras with bracket","authors":"José Manuel Casas, Emzar Khmaladze, Manuel Ladra","doi":"10.1515/forum-2023-0355","DOIUrl":"https://doi.org/10.1515/forum-2023-0355","url":null,"abstract":"We study the extensibility problem of a pair of derivations associated with an abelian extension of algebras with bracket, and derive an exact sequence of the Wells type. We introduce crossed modules for algebras with bracket and prove their equivalence with internal categories in the category of algebras with bracket. We interpret the set of equivalence classes of crossed extensions as the second cohomology. Finally, we construct an eight-term exact sequence in the cohomology of algebras with bracket.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"60 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139374734","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":"What conjugate phase retrieval complex vectors can do in quaternion Euclidean spaces","authors":"Yun-Zhang Li, Ming Yang","doi":"10.1515/forum-2023-0389","DOIUrl":"https://doi.org/10.1515/forum-2023-0389","url":null,"abstract":"Quaternion algebra &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mi&gt;ℍ&lt;/m:mi&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0389_eq_0331.png\" /&gt; &lt;jats:tex-math&gt;{mathbb{H}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is a noncommutative associative algebra. In recent years, quaternionic Fourier analysis has received increasing attention due to its applications in signal analysis and image processing. This paper addresses conjugate phase retrieval problem in the quaternion Euclidean space &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msup&gt; &lt;m:mi&gt;ℍ&lt;/m:mi&gt; &lt;m:mi&gt;M&lt;/m:mi&gt; &lt;/m:msup&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0389_eq_0330.png\" /&gt; &lt;jats:tex-math&gt;{mathbb{H}^{M}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; with &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mrow&gt; &lt;m:mi&gt;M&lt;/m:mi&gt; &lt;m:mo&gt;≥&lt;/m:mo&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0389_eq_0275.png\" /&gt; &lt;jats:tex-math&gt;{Mgeq 2}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. Write &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mi&gt;ℂ&lt;/m:mi&gt; &lt;m:mi&gt;η&lt;/m:mi&gt; &lt;/m:msub&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;{&lt;/m:mo&gt; &lt;m:mi&gt;ξ&lt;/m:mi&gt; &lt;m:mo&gt;:&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mrow&gt; &lt;m:mi&gt;ξ&lt;/m:mi&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mrow&gt; &lt;m:msub&gt; &lt;m:mi&gt;ξ&lt;/m:mi&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;/m:msub&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;β&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;η&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo rspace=\"4.2pt\"&gt;,&lt;/m:mo&gt; &lt;m:msub&gt; &lt;m:mi&gt;ξ&lt;/m:mi&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;/m:msub&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo rspace=\"4.2pt\"&gt;,&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;β&lt;/m:mi&gt; &lt;m:mo&gt;∈&lt;/m:mo&gt; &lt;m:mi&gt;ℝ&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;}&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0389_eq_0316.png\" /&gt; &lt;jats:tex-math&gt;{mathbb{C}_{eta}={xi:xi=xi_{0}+betaeta,,xi_{0},,betainmathbb{R}}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; for &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mrow&gt; &lt;m:mi&gt;η&lt;/m:mi&gt; &lt;m:mo&gt;∈&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;{&lt;/m:mo&gt; &lt;m:mi&gt;i&lt;/m:mi&gt; &lt;m:mo rspace=\"4.2pt\"&gt;,&lt;/m:mo&gt; &lt;m:mi&gt;j&lt;/m:mi&gt; &lt;m:mo rspace=\"4.2pt\"&gt;,&lt;/m:mo&gt; &lt;m:mi&gt;k&lt;/m:mi&gt; &lt;m:mo stretchy=\"false\"&gt;}&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0389_eq_0298.png\" /&gt; &lt;jats:tex-math&gt;{etain{i,,j,,k}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. We remark that not only &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"23 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139374732","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":"Topological amenability of semihypergroups","authors":"Choiti Bandyopadhyay","doi":"10.1515/forum-2022-0326","DOIUrl":"https://doi.org/10.1515/forum-2022-0326","url":null,"abstract":"In this article, we introduce and explore the notion of topological amenability in the broad setting of (locally compact) semihypergroups. We acquire several stationary, ergodic and Banach algebraic characterizations of the same in terms of convergence of certain probability measures, total variation of convolution with probability measures and translation of certain functionals, as well as the F-algebraic properties of the associated measure algebra. We further investigate the interplay between restriction of convolution product and convolution of restrictions of measures on a sub-semihypergroup. Finally, we discuss and characterize topological amenability of sub-semihypergroups in terms of certain invariance properties attained on the corresponding measure algebra of the parent semihypergroup. This in turn provides us with an affirmative answer to an open question posed by J. Wong in 1980.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"49 5 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139374999","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":"Multilinear Fourier integral operators on modulation spaces","authors":"Aparajita Dasgupta, Lalit Mohan, Shyam Swarup Mondal","doi":"10.1515/forum-2023-0158","DOIUrl":"https://doi.org/10.1515/forum-2023-0158","url":null,"abstract":"In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of weighted modulation spaces. Further, we investigate the periodic multilinear Fourier integral operator. Finally, we study continuity of bilinear pseudo-differential operators on modulation spaces for certain symbol classes, namely <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>𝐒𝐆</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0158_eq_0327.png\" /> <jats:tex-math>{mathbf{SG}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-class.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"104 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139104681","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":"Sharp Sobolev and Adams–Trudinger–Moser embeddings on weighted Sobolev spaces and their applications","authors":"João Marcos do Ó, Guozhen Lu, Raoní Ponciano","doi":"10.1515/forum-2023-0292","DOIUrl":"https://doi.org/10.1515/forum-2023-0292","url":null,"abstract":"We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths admit nontrivial solutions.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"3 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078678","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":"The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras","authors":"Dirceu Bagio, Daniel Gonçalves, Paula Savana Estácio Moreira, Johan Öinert","doi":"10.1515/forum-2023-0117","DOIUrl":"https://doi.org/10.1515/forum-2023-0117","url":null,"abstract":"Given a partial action α of a groupoid <jats:italic>G</jats:italic> on a ring <jats:italic>R</jats:italic>, we study the associated partial skew groupoid ring <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>R</m:mi> <m:msub> <m:mo>⋊</m:mo> <m:mi>α</m:mi> </m:msub> <m:mi>G</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0117_eq_0451.png\" /> <jats:tex-math>{Rrtimes_{alpha}G}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, which carries a natural <jats:italic>G</jats:italic>-grading. We show that there is a one-to-one correspondence between the <jats:italic>G</jats:italic>-invariant ideals of <jats:italic>R</jats:italic> and the graded ideals of the <jats:italic>G</jats:italic>-graded ring <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>R</m:mi> <m:msub> <m:mo>⋊</m:mo> <m:mi>α</m:mi> </m:msub> <m:mi>G</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0117_eq_0451.png\" /> <jats:tex-math>{Rrtimes_{alpha}G}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. We provide sufficient conditions for primeness, and necessary and sufficient conditions for simplicity of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>R</m:mi> <m:msub> <m:mo>⋊</m:mo> <m:mi>α</m:mi> </m:msub> <m:mi>G</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0117_eq_0451.png\" /> <jats:tex-math>{Rrtimes_{alpha}G}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. We show that every ideal of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>R</m:mi> <m:msub> <m:mo>⋊</m:mo> <m:mi>α</m:mi> </m:msub> <m:mi>G</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0117_eq_0451.png\" /> <jats:tex-math>{Rrtimes_{alpha}G}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is graded if and only if α has the residual intersection property. Furthermore, if α is induced by a topological partial action θ, then we prove that minimality of θ is equivalent to <jats:italic>G</jats:italic>-simplicity of <jats:italic>R</jats:italic>, topological transitivity of θ is equivalent to <jats:italic>G</jats:italic>-primeness of <jats:italic>R</jats:italic>, and topological freeness of θ on every closed invariant subset of the underlying topological space is equivalent to α having the residual intersection property. As an application, we characterize condition (K) for an ultragraph in terms of topological properties of the associated partial action and in terms of algebraic properties of the associated ultragraph algebra.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"4 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078565","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":"Spectral invariance of quasi-Banach algebras of matrices and pseudodifferential operators","authors":"Karlheinz Gröchenig, Christine Pfeuffer, Joachim Toft","doi":"10.1515/forum-2023-0212","DOIUrl":"https://doi.org/10.1515/forum-2023-0212","url":null,"abstract":"We extend the stability and spectral invariance of convolution-dominated matrices to the case of quasi-Banach algebras <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>p</m:mi> <m:mo>&lt;</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2023-0212_eq_0605.png\" /> <jats:tex-math>{p&lt;1}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. As an application, we construct a spectrally invariant quasi-Banach algebra of pseudodifferential operators with non-smooth symbols that generalize Sjöstrand’s results.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"27 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078615","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":"L-series of weakly holomorphic quasimodular forms and a converse theorem","authors":"Mrityunjoy Charan","doi":"10.1515/forum-2023-0194","DOIUrl":"https://doi.org/10.1515/forum-2023-0194","url":null,"abstract":"We define <jats:italic>L</jats:italic>-series of weakly holomorphic quasimodular forms and we derive functional equations of those <jats:italic>L</jats:italic>-series. We also prove a converse theorem for weakly holomorphic quasimodular forms.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"4 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078620","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}