Pub Date : 2026-02-04DOI: 10.1016/j.jmaa.2026.130486
Shenghao Li , Xin Yang
We prove the local well-posedness of the initial boundary value problem for the nonlinear quadratic Schrödinger equation under low initial-boundary regularity assumptions via the boundary integral operator method introduced by Bona-Sun-Zhang [4]. The key ingredient in our study is to generalize a special extension for the boundary integral operator which can fit lower regularity assumptions in spaces comparing to the “zero” extension approach introduced in [13].
{"title":"A lower index bilinear estimate for the quadratic Schrödinger equation and application for its half line problem","authors":"Shenghao Li , Xin Yang","doi":"10.1016/j.jmaa.2026.130486","DOIUrl":"10.1016/j.jmaa.2026.130486","url":null,"abstract":"<div><div>We prove the local well-posedness of the initial boundary value problem for the nonlinear quadratic Schrödinger equation under low initial-boundary regularity assumptions via the boundary integral operator method introduced by Bona-Sun-Zhang <span><span>[4]</span></span>. The key ingredient in our study is to generalize a special extension for the boundary integral operator which can fit lower regularity assumptions in <span><math><msup><mrow><mi>X</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>b</mi></mrow></msup></math></span> spaces comparing to the “zero” extension approach introduced in <span><span>[13]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"560 1","pages":"Article 130486"},"PeriodicalIF":1.2,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122688","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}
Pub Date : 2026-01-27DOI: 10.1016/j.jmaa.2026.130464
Yuyou Zhong , Qi Wang , Chungen Liu
In this paper, we investigate a class of non-autonomous high-dimensional differential systems with distributed delay. By exploiting the equivalence between finding periodic solutions for such systems under symmetric boundary conditions and solving an associated first-order Hamiltonian system, we establish novel multiplicity results. These results are obtained through a combination of symmetric index theory and critical point theory.
{"title":"Multiple symmetric periodic solutions of distributed delay differential systems via Hamiltonian systems","authors":"Yuyou Zhong , Qi Wang , Chungen Liu","doi":"10.1016/j.jmaa.2026.130464","DOIUrl":"10.1016/j.jmaa.2026.130464","url":null,"abstract":"<div><div>In this paper, we investigate a class of non-autonomous high-dimensional differential systems with distributed delay. By exploiting the equivalence between finding periodic solutions for such systems under symmetric boundary conditions and solving an associated first-order Hamiltonian system, we establish novel multiplicity results. These results are obtained through a combination of symmetric index theory and critical point theory.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130464"},"PeriodicalIF":1.2,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057485","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}
Pub Date : 2026-01-22DOI: 10.1016/j.jmaa.2026.130440
Ryan L. Acosta Babb
It is known that the Bessel–Fourier coefficients of a function f, such that is integrable over with , satisfy . We show a partial converse, namely that for and any non-negative , there is a function f such that is integrable and its Bessel–Fourier coefficients satisfy and . For , we conjecture that the same should be true when , and discuss some consequences of this conjecture for the divergence Bessel–Fourier expansions of radial functions on the disc.
{"title":"On the rate of growth of Bessel–Fourier coefficients for integrable functions","authors":"Ryan L. Acosta Babb","doi":"10.1016/j.jmaa.2026.130440","DOIUrl":"10.1016/j.jmaa.2026.130440","url":null,"abstract":"<div><div>It is known that the Bessel–Fourier coefficients <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub></math></span> of a function <em>f</em>, such that <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>s</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is integrable over <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> with <span><math><mn>0</mn><mo>⩽</mo><mi>s</mi><mo>⩽</mo><mi>ν</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span>, satisfy <span><math><msubsup><mrow><mi>j</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow><mrow><mo>−</mo><mi>s</mi><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub><mo>→</mo><mn>0</mn></math></span>. We show a partial converse, namely that for <span><math><mn>0</mn><mo>⩽</mo><mi>α</mi><mo><</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span> and any non-negative <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>→</mo><mn>0</mn></math></span>, there is a function <em>f</em> such that <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>α</mi><mo>+</mo><mn>1</mn><mo>+</mo><mi>ν</mi></mrow></msup><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is integrable and its Bessel–Fourier coefficients <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub></math></span> satisfy <span><math><msubsup><mrow><mi>j</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub><mo>⩾</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> and <span><math><msubsup><mrow><mi>j</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>m</mi></mrow></msub><mo>→</mo><mn>0</mn></math></span>. For <span><math><mi>ν</mi><mo>=</mo><mn>0</mn></math></span>, we conjecture that the same should be true when <span><math><mi>α</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, and discuss some consequences of this conjecture for the divergence Bessel–Fourier expansions of radial functions on the disc.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130440"},"PeriodicalIF":1.2,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024435","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}
Pub Date : 2026-01-22DOI: 10.1016/j.jmaa.2026.130456
Elismar R. Oliveira , Rafael R. Souza
In this work we present iterated function systems with general measures (IFSm) formed by a set of maps acting on a compact space X, for a compact space of indices, Λ. The Markov process associated with the IFS iteration is defined using a general family of probability measures on Λ, where : is given by , with λ randomly chosen according to . We prove the existence of the topological attractor and the existence of the invariant attracting measure for the Markov Process. We also prove that the support of the invariant measure is given by the attractor and results on the stochastic stability of the invariant measures, with respect to changes in the family .
{"title":"The Hutchinson-Barnsley theory for iterated function systems with general measures","authors":"Elismar R. Oliveira , Rafael R. Souza","doi":"10.1016/j.jmaa.2026.130456","DOIUrl":"10.1016/j.jmaa.2026.130456","url":null,"abstract":"<div><div>In this work we present iterated function systems with general measures (IFSm) formed by a set of maps <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> acting on a compact space <em>X</em>, for a compact space of indices, Λ. The Markov process <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> associated with the IFS iteration is defined using a general family of probability measures <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> on Λ, where <span><math><mi>x</mi><mo>∈</mo><mi>X</mi></math></span>: <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> is given by <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></math></span>, with <em>λ</em> randomly chosen according to <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span>. We prove the existence of the topological attractor and the existence of the invariant attracting measure for the Markov Process. We also prove that the support of the invariant measure is given by the attractor and results on the stochastic stability of the invariant measures, with respect to changes in the family <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130456"},"PeriodicalIF":1.2,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079639","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}
Pub Date : 2026-01-22DOI: 10.1016/j.jmaa.2026.130459
Qian Ma, Shanbing Li
This paper investigates the coexistence states of a diffusive Lotka-Volterra prey-predator model incorporating both hunting cooperation among predators and a prey-taxis mechanism, subject to homogeneous Dirichlet boundary conditions. By establishing a priori estimates for coexistence states, including -bounds and -bounds, we derive sufficient conditions for the existence and non-existence of coexistence states in the general case with arbitrary diffusion and sensitivity coefficients. Particularly, we construct a bifurcation branch (connected set) of coexistence states linking two semi-trivial solutions and determine the bifurcation direction near the bifurcation point.
{"title":"Coexistence states in a prey-taxis system with hunting cooperation","authors":"Qian Ma, Shanbing Li","doi":"10.1016/j.jmaa.2026.130459","DOIUrl":"10.1016/j.jmaa.2026.130459","url":null,"abstract":"<div><div>This paper investigates the coexistence states of a diffusive Lotka-Volterra prey-predator model incorporating both hunting cooperation among predators and a prey-taxis mechanism, subject to homogeneous Dirichlet boundary conditions. By establishing a <em>priori</em> estimates for coexistence states, including <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-bounds and <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>p</mi></mrow></msup></math></span>-bounds, we derive sufficient conditions for the existence and non-existence of coexistence states in the general case with arbitrary diffusion and sensitivity coefficients. Particularly, we construct a bifurcation branch (connected set) of coexistence states linking two semi-trivial solutions and determine the bifurcation direction near the bifurcation point.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130459"},"PeriodicalIF":1.2,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078036","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}
Pub Date : 2026-01-22DOI: 10.1016/j.jmaa.2026.130457
Abbas Najati, Mohammad Amin Tareeghee
In this paper, we investigate a Jensen-type version of Dhombres' functional equation, namely for functions , where and are uniquely 2-divisible abelian groups. We also investigate the superstability behavior of this functional equation.
{"title":"A Jensen-type variant of Dhombres' functional equation and its superstability","authors":"Abbas Najati, Mohammad Amin Tareeghee","doi":"10.1016/j.jmaa.2026.130457","DOIUrl":"10.1016/j.jmaa.2026.130457","url":null,"abstract":"<div><div>In this paper, we investigate a Jensen-type version of Dhombres' functional equation, namely<span><span><span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>≠</mo><mn>0</mn><mo>⇒</mo><mn>2</mn><mi>f</mi><mrow><mo>(</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>G</mi></math></span></span></span> for functions <span><math><mi>f</mi><mo>:</mo><mi>G</mi><mo>→</mo><mi>V</mi></math></span>, where <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mo>+</mo><mo>)</mo></math></span> and <span><math><mo>(</mo><mi>V</mi><mo>,</mo><mo>+</mo><mo>)</mo></math></span> are uniquely 2-divisible abelian groups. We also investigate the superstability behavior of this functional equation.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130457"},"PeriodicalIF":1.2,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079720","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}
Pub Date : 2026-01-22DOI: 10.1016/j.jmaa.2026.130454
Long Guo, Jingyu Jia
In this paper, we study the energy conservation of weak solution to the incompressible viscoelastic equations in a bounded domain. When the coefficient of viscosity , energy equality is proved under some global Hölder regularity condition for the velocity u and deformation tensor F. When , we proved that some global integrability condition for and suitable integrability conditions near the boundary for the pressure p are sufficient for the energy equality.
{"title":"Energy conservation for weak solution of incompressible viscoelastic fluids in bounded domain","authors":"Long Guo, Jingyu Jia","doi":"10.1016/j.jmaa.2026.130454","DOIUrl":"10.1016/j.jmaa.2026.130454","url":null,"abstract":"<div><div>In this paper, we study the energy conservation of weak solution to the incompressible viscoelastic equations in a bounded domain. When the coefficient of viscosity <span><math><mi>μ</mi><mo>=</mo><mn>0</mn></math></span>, energy equality is proved under some global Hölder regularity condition for the velocity <strong><em>u</em></strong> and deformation tensor <strong><em>F</em></strong>. When <span><math><mi>μ</mi><mo>></mo><mn>0</mn></math></span>, we proved that some global integrability condition for <span><math><mo>(</mo><mi>u</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> and suitable integrability conditions near the boundary for the pressure <em>p</em> are sufficient for the energy equality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130454"},"PeriodicalIF":1.2,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057486","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}
Pub Date : 2026-01-22DOI: 10.1016/j.jmaa.2026.130455
Viktor Feruk
In this paper, we study a system of weakly nonlinear fractional differential equations with tempered Caputo derivative. The solutions of this system satisfy the conditions in the form of a bounded weakly nonlinear vector functional. It is assumed that the linear inhomogeneous generating boundary-value problem possesses a family of solutions. The necessary and sufficient conditions for the existence of solutions have been obtained, which at turn into one of the solutions of the generating problem. An iterative algorithm for building such solutions is proposed. The results obtained by us generalize the known results of the theory of ordinary differential equations and are also new for the case of the Caputo derivative.
{"title":"Boundary-value problem for a system of fractional differential equations with tempered Caputo derivative","authors":"Viktor Feruk","doi":"10.1016/j.jmaa.2026.130455","DOIUrl":"10.1016/j.jmaa.2026.130455","url":null,"abstract":"<div><div>In this paper, we study a system of weakly nonlinear fractional differential equations with tempered Caputo derivative. The solutions of this system satisfy the conditions in the form of a bounded weakly nonlinear vector functional. It is assumed that the linear inhomogeneous generating boundary-value problem possesses a family of solutions. The necessary and sufficient conditions for the existence of solutions have been obtained, which at <span><math><mi>ε</mi><mo>=</mo><mn>0</mn></math></span> turn into one of the solutions of the generating problem. An iterative algorithm for building such solutions is proposed. The results obtained by us generalize the known results of the theory of ordinary differential equations and are also new for the case of the Caputo derivative.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130455"},"PeriodicalIF":1.2,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078039","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}
Pub Date : 2026-01-22DOI: 10.1016/j.jmaa.2026.130453
Wenqiang Zhao , Xia Liu
This article is concerned with the random dynamics of non-autonomous stochastic reaction-diffusion equations that incorporate additive white noise and infinite delay, with the delay term being globally Lipschitz continuous. We first establish the existence of (periodic) pullback random attractors for the corresponding non-autonomous dynamical system (NRDS). The asymptotical compactness of solutions is primarily achieved by applying the Arzelà-Ascoli theorem over a compact time interval, coupled with a limiting argument for the negative infinite part. Furthermore, we demonstrate that the solution to the underlying equations is jointly continuous in both the initial time and the initial data. This result allows us to construct a family of (periodic) invariant Borel probability measures that are supported within the pullback random attractors for the NRDS.
{"title":"Invariant measure of non-autonomous stochastic reaction-diffusion equations with infinite delay and additive white noise","authors":"Wenqiang Zhao , Xia Liu","doi":"10.1016/j.jmaa.2026.130453","DOIUrl":"10.1016/j.jmaa.2026.130453","url":null,"abstract":"<div><div>This article is concerned with the random dynamics of non-autonomous stochastic reaction-diffusion equations that incorporate additive white noise and infinite delay, with the delay term being globally Lipschitz continuous. We first establish the existence of (periodic) pullback random attractors for the corresponding non-autonomous dynamical system (NRDS). The asymptotical compactness of solutions is primarily achieved by applying the Arzelà-Ascoli theorem over a compact time interval, coupled with a limiting argument for the negative infinite part. Furthermore, we demonstrate that the solution to the underlying equations is jointly continuous in both the initial time and the initial data. This result allows us to construct a family of (periodic) invariant Borel probability measures that are supported within the pullback random attractors for the NRDS.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"558 1","pages":"Article 130453"},"PeriodicalIF":1.2,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078041","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}
Pub Date : 2026-01-21DOI: 10.1016/j.jmaa.2026.130446
Josiah Aakre
Many previously studied path algebras and self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid is simple. We show that the simplicity of the reduced -algebra of a contracting self-similar groupoid coincides with the simplicity of the Steinberg algebra. As an aside, we show that simplicity of the two algebras sometimes depends only on the skeleton of the self-similar groupoid acting on a strongly connected graph. Finally, we apply our methods to examples including a self-similar groupoid akin to multispinal self-similar groups and a self-similar groupoid built from the well-known Basilica group.
{"title":"Simplicity of algebras and C⁎-algebras of self-similar groupoids","authors":"Josiah Aakre","doi":"10.1016/j.jmaa.2026.130446","DOIUrl":"10.1016/j.jmaa.2026.130446","url":null,"abstract":"<div><div>Many previously studied path algebras and self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid is simple. We show that the simplicity of the reduced <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra of a contracting self-similar groupoid coincides with the simplicity of the Steinberg algebra. As an aside, we show that simplicity of the two algebras sometimes depends only on the skeleton of the self-similar groupoid acting on a strongly connected graph. Finally, we apply our methods to examples including a self-similar groupoid akin to multispinal self-similar groups and a self-similar groupoid built from the well-known Basilica group.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 1","pages":"Article 130446"},"PeriodicalIF":1.2,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146024432","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}
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