Indagationes Mathematicae-New Series最新文献

{"title":"Invariant classes for families of complexes","authors":"Daniel Levin,&nbsp;Alexander Zuevsky","doi":"10.1016/j.indag.2026.02.001","DOIUrl":"10.1016/j.indag.2026.02.001","url":null,"abstract":"<div><div>We consider families of double infinite complexes <span><math><mi>C</mi></math></span> of spaces with elements depending on a number of parameters, and endowed with a converging associative multiple product. The existence of left/right local/non-local square-vanishing ideals is assumed for subspaces of <span><math><mi>C</mi></math></span>-spaces. We show that a set of differential and orthogonality relations together with coherence conditions on indices of a chain-cochain complex <span><math><mi>C</mi></math></span> elements generates families of graded differential algebras. With the appropriate orthogonality conditions on completions of <span><math><mi>C</mi></math></span> elements in the multiple product, we define the equivalence classes of cohomology invariants.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1812-1833"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916912","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}

{"title":"Essential self-adjointness of non-semibounded Schrödinger operators on infinite graphs","authors":"Ognjen Milatovic","doi":"10.1016/j.indag.2026.01.005","DOIUrl":"10.1016/j.indag.2026.01.005","url":null,"abstract":"<div><div>We work in the setting of infinite, not necessarily locally finite, weighted graphs. We give a sufficient condition for the essential self-adjointness of (discrete) Schrödinger operators <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>V</mi></mrow></msub></math></span> that are not necessarily lower semi-bounded. As a corollary of the main result, we show that <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>V</mi></mrow></msub></math></span> is essentially self-adjoint if the potential <span><math><mi>V</mi></math></span> satisfies <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≥</mo><mo>−</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>ρ</mi><mrow><mo>(</mo><mi>o</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>, for all vertices <span><math><mrow><mi>x</mi><mo>∈</mo><mi>X</mi></mrow></math></span>, where <span><math><mi>o</mi></math></span> is a fixed vertex, <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are non-negative constants, and <span><math><mi>ρ</mi></math></span> is an intrinsic metric satisfying the condition (B*): restriction of the weighted vertex degree to every ball corresponding to <span><math><mi>ρ</mi></math></span> is bounded (not necessarily uniformly bounded). Furthermore, we show that <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>V</mi></mrow></msub></math></span> is essentially self-adjoint if <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≥</mo><mo>−</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mrow><mo>[</mo><mi>ρ</mi><mrow><mo>(</mo><mi>o</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>]</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span> for all <span><math><mrow><mi>x</mi><mo>∈</mo><mi>X</mi></mrow></math></span>, where <span><math><mi>o</mi></math></span> is a fixed vertex, <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are non-negative constants, and <span><math><mi>ρ</mi></math></span> is an intrinsic metric having a finite jump size and satisfying the condition (B*).</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1797-1811"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916970","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}

{"title":"L- and M-weakly compact multilinear operators and their linear adjoints","authors":"Geraldo Botelho,&nbsp;Ariel Monção","doi":"10.1016/j.indag.2026.02.004","DOIUrl":"10.1016/j.indag.2026.02.004","url":null,"abstract":"<div><div>Let <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>m</mi></mrow></msub></mrow></math></span> be Banach spaces and let <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>,</mo><mi>F</mi></mrow></math></span> be Banach lattices. Our main results read as follows: (i) The linear adjoint <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> of a continuous multilinear operator <span><math><mrow><mi>A</mi><mo>:</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><mo>⋯</mo><mo>×</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>→</mo><mi>F</mi></mrow></math></span> is <span><math><mi>M</mi></math></span>-weakly compact if and only if <span><math><mi>A</mi></math></span> is <span><math><mi>L</mi></math></span>-weakly compact. (ii) The linear adjoint <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> of a multilinear operator of order bounded variation <span><math><mrow><mi>A</mi><mo>:</mo><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><mo>⋯</mo><mo>×</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>→</mo><mi>F</mi></mrow></math></span> is <span><math><mi>L</mi></math></span>-weakly compact if and only if the linearization of <span><math><mi>A</mi></math></span> on the positive projective tensor product is <span><math><mi>M</mi></math></span>-weakly compact. In our way to prove these results, we develop the basic theory of linear adjoints of multilinear operators between Riesz spaces, we prove that multilinear operators of order bounded variation between Banach lattices are continuous, and we explore different notions of multilinear operators of <span><math><mi>M</mi></math></span>-weakly compact-type.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1862-1882"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916871","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}

{"title":"Sign changes in Fourier coefficients of the symmetric power L-functions on sums of two squares","authors":"Amrinder Kaur","doi":"10.1016/j.indag.2025.12.005","DOIUrl":"10.1016/j.indag.2025.12.005","url":null,"abstract":"<div><div>Let <span><math><mi>f</mi></math></span> be a normalized Hecke eigen cusp form of even integral weight <span><math><mi>k</mi></math></span> for the full modular group <span><math><mrow><mi>S</mi><mi>L</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>Z</mi><mo>)</mo></mrow></mrow></math></span>. For integers <span><math><mrow><mi>j</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, let <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><msup><mrow><mi>Sym</mi></mrow><mrow><mi>j</mi></mrow></msup><mi>f</mi></mrow></msub><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></math></span> denote the <span><math><mi>m</mi></math></span>th Fourier coefficient of the <span><math><mi>j</mi></math></span>th symmetric power <span><math><mi>L</mi></math></span>-function associated with <span><math><mi>f</mi></math></span>. We give a quantitative result on the number of sign changes of <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><msup><mrow><mi>Sym</mi></mrow><mrow><mi>j</mi></mrow></msup><mi>f</mi></mrow></msub><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></math></span> for the indices <span><math><mi>m</mi></math></span> that are the sum of two squares in the interval <span><math><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>]</mo></mrow></math></span> for sufficiently large <span><math><mi>x</mi></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1712-1724"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916962","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}

{"title":"Purely exponential Diophantine equations with four terms of consecutive bases: Contribution to Skolem’s conjecture","authors":"Maohua Le,&nbsp;Takafumi Miyazaki","doi":"10.1016/j.indag.2026.02.003","DOIUrl":"10.1016/j.indag.2026.02.003","url":null,"abstract":"<div><div>We study purely exponential Diophantine equations with four terms of consecutive bases. Notably, we prove that all solutions to the equation <span><span><span><math><mrow><msup><mrow><mi>n</mi></mrow><mrow><mi>x</mi></mrow></msup><mo>=</mo><msup><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mi>y</mi></mrow></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mrow><mrow><mi>z</mi></mrow></msup><mo>+</mo><msup><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mrow><mrow><mi>w</mi></mrow></msup></mrow></math></span></span></span>in positive integers <span><math><mrow><mi>n</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></mrow></math></span> and <span><math><mi>w</mi></math></span> are given by <span><math><mrow><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>w</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mn>2,5,1,1,2</mn><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mo>(</mo><mn>3,3,2,1,1</mn><mo>)</mo></mrow></math></span>. Our proof of this result for each <span><math><mrow><mi>n</mi><mo>≥</mo><mn>4</mn></mrow></math></span> provides an explicit modulus <span><math><mi>M</mi></math></span> such that the corresponding equation has no solution already modulo <span><math><mi>M</mi></math></span>. This contributes to a classical problem posed by T. Skolem in 1930’s on a local–global principle for purely exponential Diophantine equations.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1849-1861"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916869","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}

{"title":"Topological center of the double dual of the Orlicz Figà-Talamanca Herz algebra","authors":"Arvish Dabra,&nbsp;N. Shravan Kumar","doi":"10.1016/j.indag.2025.12.004","DOIUrl":"10.1016/j.indag.2025.12.004","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; be a locally compact group and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;Ψ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; be a complementary pair of Young functions. Let &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; denote the Orlicz analogue of the classical Figà-Talamanca Herz algebra &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and let &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Λ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; represent the topological center of the double dual of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with respect to the first Arens product. In this article, we show that the problem of determining the strong Arens irregularity of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; can be reduced to the case of open &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;compact groups. More precisely, we establish that &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Λ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; if and only if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Λ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for every open &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;compact subgroup &lt;span&gt;&lt;math&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is amenable and &lt;span&gt;&lt;math&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; satisfies the MA condition. Furthermore, we obtain an analogous result for the topological center of the algebra &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ψ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̂&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; Finally, we prove several results concerning the semi-simplicity of the Banach algebras &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1697-1711"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916965","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}

{"title":"The Cesàro operator on local Dirichlet spaces","authors":"E. Dellepiane,&nbsp;J. Mashreghi,&nbsp;M. Nasri,&nbsp;W. Verreault","doi":"10.1016/j.indag.2026.02.005","DOIUrl":"10.1016/j.indag.2026.02.005","url":null,"abstract":"<div><div>The family of Cesàro operators <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span>, <span><math><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>[</mo><mn>0,1</mn><mo>]</mo></mrow></mrow></math></span>, consists of finite rank operators on Banach spaces of analytic functions on the open unit disc. In this work, we investigate these operators as they act on the local Dirichlet spaces <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>ζ</mi></mrow></msub></math></span>. It is well-established that they provide a linear approximation scheme when <span><math><mrow><mi>α</mi><mo>&gt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>, with the threshold value <span><math><mrow><mi>α</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span> being optimal. We strengthen this result by deriving precise asymptotic values for the norm of these operators when <span><math><mrow><mi>α</mi><mo>≤</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>, corresponding to the breakdown of approximation schemes. Additionally, we establish upper and lower estimates for the norm when <span><math><mrow><mi>α</mi><mo>&gt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1883-1896"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916872","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}

{"title":"Embedding Higman–Thompson groups of unfolding trees into the Leavitt path algebras","authors":"Roman Gorazd","doi":"10.1016/j.indag.2026.03.001","DOIUrl":"10.1016/j.indag.2026.03.001","url":null,"abstract":"<div><div>The isomorphism problem of regular Higman–Thompson groups was solved in Pardo (2011), via embedding it into the Leavitt algebra. In this paper, we will expand these results to embed the Higman–Thompson groups of unfolding trees of directed graphs (also known as full groups of one-sided shifts) into the Leavitt path algebra. This embedding allows us to show that any isomorphism of rooted Leavitt path algebras over <span><math><mi>Z</mi></math></span> induces an isomorphism between Higman–Thompson groups.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1897-1916"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916868","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}

{"title":"The interplay between additive and multiplicative central sets theorems","authors":"Pintu Debnath,&nbsp;Sayan Goswami,&nbsp;Chunlin Liu","doi":"10.1016/j.indag.2026.01.002","DOIUrl":"10.1016/j.indag.2026.01.002","url":null,"abstract":"<div><div>The concept of central sets, introduced by Furstenberg through the framework of topological dynamics, has played a pivotal role in combinatorial number theory. Furstenberg’s Central Sets Theorem highlighted their rich combinatorial structure. Later in [Fund. Math., 199 (2008), 155–175.], De, Hindman, and Strauss strengthen this theorem using the algebraic framework of the Stone–Čech compactification. In this article, we establish a unified version of the Central Sets Theorem that simultaneously captures both additive and multiplicative structures.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1733-1741"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916967","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}

{"title":"Sparse random graphs with many triangles","authors":"Suman Chakraborty,&nbsp;Remco van der Hofstad,&nbsp;Frank den Hollander","doi":"10.1016/j.indag.2026.01.003","DOIUrl":"10.1016/j.indag.2026.01.003","url":null,"abstract":"<div><div>In this paper we consider the Erdős–Rényi random graph in the sparse regime in the limit as the number of vertices <span><math><mi>n</mi></math></span> tends to infinity. We are interested in what this graph looks like when it contains many triangles, in two settings. First, we derive asymptotically sharp bounds on the probability that the graph contains a large number of triangles. We show that, conditionally on this event, with high probability the graph contains an almost complete subgraph, i.e., the triangles form a near-clique, and has the <em>same</em> local limit as the original Erdős–Rényi random graph. Second, we derive asymptotically sharp bounds on the probability that the graph contains a large number of vertices that are part of a triangle. If order <span><math><mi>n</mi></math></span> vertices are in triangles, then the local limit (provided it exists) is <em>different</em> from that of the Erdős–Rényi random graph. Our results shed light on the challenges that arise in the description of real-world networks, which often are <em>sparse, yet highly clustered</em>, and on exponential random graphs, which often are used to model such networks.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 5","pages":"Pages 1742-1775"},"PeriodicalIF":0.8,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148916968","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}