Journal of Mathematical Analysis and Applications最新文献

{"title":"Zeros of random Müntz polynomials","authors":"Doron S. Lubinsky ,&nbsp;Igor E. Pritsker","doi":"10.1016/j.jmaa.2025.129799","DOIUrl":"10.1016/j.jmaa.2025.129799","url":null,"abstract":"<div><div>We study the expected number of positive zeros of Müntz polynomials with real i.i.d. coefficients. For the standard Gaussian coefficients, we establish asymptotic results for the expected number of positive zeros when the exponents of Müntz monomials that span our random Müntz polynomials have polynomial and logarithmic growth. We also present many bounds on the expected number of zeros of random Müntz polynomials with various real i.i.d. coefficients, including the case of arbitrary nontrivial real i.i.d. coefficients. Since Müntz polynomials include lacunary polynomials, sparse polynomials or fewnomials as special cases, our results directly apply to the expected number of real zeros for those classes of polynomials with gaps.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129799"},"PeriodicalIF":1.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314467","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":"Algebraic properties of Toeplitz + Hankel operators","authors":"Caixing Gu","doi":"10.1016/j.jmaa.2025.129797","DOIUrl":"10.1016/j.jmaa.2025.129797","url":null,"abstract":"<div><div>Recently an elegant result of Sang <span><span>[29]</span></span> characterizes when the product of two Toeplitz + Hankel operators is a Toeplitz + Hankel operator ((T+H)-operator). This result unifies several product problems for Toeplitz and Hankel operators. We extend the method of the author <span><span>[19]</span></span> on product problems for block Toeplitz and Hankel operators to give a short proof and some refinements of the result of Sang. Furthermore, we identify (T+H)-operators which are isometries or unitaries. We characterize when two arbitrary (T+H)-operators commute. We introduce several classes of (T+H)-operators which extend some classes of (T+H)-operators studied by Basor and Ehrhardt <span><span>[2]</span></span> <span><span>[3]</span></span> and Sang <span><span>[29]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129797"},"PeriodicalIF":1.2,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270216","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":"On the regularity of solutions to a class of nonlocal evolution equations with sectorial operators","authors":"Nguyen Van Dac ,&nbsp;Tran Dinh Ke ,&nbsp;Pham Anh Toan","doi":"10.1016/j.jmaa.2025.129798","DOIUrl":"10.1016/j.jmaa.2025.129798","url":null,"abstract":"<div><div>We deal with an abstract model of nonlocal evolution equations with sectorial operators and nonlinear perturbations. Regularity estimates for resolvent families are derived through semigroup representation, which allow us to show a global solvability for the associated Cauchy problem in fractional power spaces. Employing fixed point argument and resolvent theory, we obtain a Hölder regularity result for the mentioned problem. Then the analytic resolvent theory is utilized to demonstrate that the obtained solution is a strong one under appropriate conditions. An application to a class of nonlinear subdiffusion equations in the whole space is given.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129798"},"PeriodicalIF":1.2,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271349","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":"Shrinking bounded domains to totally bounded ones","authors":"Mihály Bessenyei ,&nbsp;Evelin Pénzes","doi":"10.1016/j.jmaa.2025.129808","DOIUrl":"10.1016/j.jmaa.2025.129808","url":null,"abstract":"<div><div>The Kuratowski measure of noncompactness or the measure of nondensifiability provide direct approach to topological fixed point theorems or to existence issues of generalized fractals. We point out that these measures are not so distinguished as they appear at first glance: Requiring quite simple properties on a set-function, we can prove analogous results. The method behind (the main result of this note) is a reducing principle which allows to shrink bounded and closed domains to compact ones. In the approach, the Knaster–Tarski and the Kantorovich Fixed Point Theorems play a key role.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129808"},"PeriodicalIF":1.2,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314637","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":"A multifractal analysis for uniform level sets with constraints on word appearance","authors":"Ziyu Liu","doi":"10.1016/j.jmaa.2025.129793","DOIUrl":"10.1016/j.jmaa.2025.129793","url":null,"abstract":"<div><div>Given a topologically transitive subshift of finite type, the <em>u</em>-dimension of the level sets of the quotient of Birkhoff sums is a well-studied topic. In this paper, we consider what we shall call the uniform level sets, which are subsets of the level sets. We shall show that the <em>α</em>-level set and the uniform <em>α</em>-level set have the same <em>u</em>-dimension. Moreover, we also consider two types of subsets of the uniform level sets, whose elements satisfy certain constraints on their subwords in addition. We shall show that for <em>α</em> not on the boundary of the dimension spectrum, these subsets of the uniform <em>α</em>-level set also have the same <em>u</em>-dimension as the <em>α</em>-level set. As an application, we shall perform a multifractal analysis of the Hölder regularity of a Gibbs measure on a one-dimensional manifold.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129793"},"PeriodicalIF":1.2,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271348","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":"Li-Yorke chaos of wave equations with linear boundary conditions under the weak topology","authors":"Qigui Yang,&nbsp;Pengxian Zhu","doi":"10.1016/j.jmaa.2025.129789","DOIUrl":"10.1016/j.jmaa.2025.129789","url":null,"abstract":"<div><div>The initial and boundary value problem for a one-dimensional wave equation on a Hilbert space is investigated. The Dirichlet, Neumann and Robin boundary conditions are systematically analyzed. When the Hilbert space is equipped with a weak topology that induced by the bounded linear functionals, the initial and boundary value problems have been rigorously proven to exhibit Li-Yorke chaos. The existence of a pair of conjugate pure imaginary eigenvalues in the linear operator induced from the wave equation is demonstrated to cause weak Li-Yorke chaos. However, they show stability when the weak topology is replaced by the norm topology. This interesting discovery reveals a remarkable phenomenon that the topology of the infinite-dimensional space is a crucial factor determining chaos of the linear hyperbolic PDEs. Furthermore, it illustrates that the infinite-dimensional dynamical systems governed by PDEs can be simple in form and still have chaotic complexity.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129789"},"PeriodicalIF":1.2,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144290713","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":"Error estimates for interpolation by harmonic and biharmonic splines with annular geometry","authors":"Ognyan Kounchev ,&nbsp;Hermann Render ,&nbsp;Tsvetomir Tsachev","doi":"10.1016/j.jmaa.2025.129795","DOIUrl":"10.1016/j.jmaa.2025.129795","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The main result in this paper is an error estimate for interpolation by biharmonic splines in an annulus &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&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;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, with respect to a partition by concentric annular domains &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for radii &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. The biharmonic splines interpolate a smooth function on the spheres &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&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;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and satisfy Dirichlet boundary conditions for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&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;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&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;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. It is a remarkable fact that an elegant technique in the one-dimensional spline theory, namely a special orthogonality relation for the error, can be carried over to the case of biharmonic splines leading to an elegant proof. For the error estimates it is important to determine the smallest constant &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; among all constants &lt;em&gt;c&lt;/em&gt; satisfying&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;munder&gt;&lt;mi&gt;sup&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;munder&gt;&lt;mi&gt;sup&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; for all &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; vanishing on the boundary of the bounded domain Ω. In this paper we describe &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mro","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129795"},"PeriodicalIF":1.2,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321294","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 sample-path dynamics of a stochastic Holling-II type slow-fast predator-prey system","authors":"Ping Li ,&nbsp;Yiliu Wang","doi":"10.1016/j.jmaa.2025.129791","DOIUrl":"10.1016/j.jmaa.2025.129791","url":null,"abstract":"<div><div>In this paper, we consider the effect of small (but not exponentially small) additive noise on the trajectories of a Holling-II type slow-fast predator-prey system, which admits a turning point, a fold point, and a unique limit cycle. We quantitatively describe the sample-path dynamics of the stochastic predator-prey system by estimating the probability that the perturbed stochastic paths stay in some tubular neighborhood of the deterministic orbits.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129791"},"PeriodicalIF":1.2,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144314636","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":"Preservers of operator commutativity","authors":"Gerardo M. Escolano ,&nbsp;Antonio M. Peralta ,&nbsp;Armando R. Villena","doi":"10.1016/j.jmaa.2025.129796","DOIUrl":"10.1016/j.jmaa.2025.129796","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; be JBW&lt;sup&gt;⁎&lt;/sup&gt;-algebras admitting no central summands of type &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, and let &lt;span&gt;&lt;math&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; be a linear bijection preserving operator commutativity in both directions, that is,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;⇔&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; for all &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, where the associator of three elements &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; in &lt;span&gt;&lt;math&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is defined by &lt;span&gt;&lt;math&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. We prove that under these conditions there exist a unique invertible central element &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; in &lt;span&gt;&lt;math&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, a unique Jordan isomorphism &lt;span&gt;&lt;math&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, and a unique linear mapping &lt;em&gt;β&lt;/em&gt; from &lt;span&gt;&lt;math&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; to the centre of &lt;span&gt;&lt;math&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; satisfying&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; for all &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. Furthermore, if Φ is a symmetric mapping (i.e., &lt;span&gt;&lt;math&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&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;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; for all &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;), the element &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is self-adjoint, &lt;em&gt;J&lt;/em&gt; is a Jordan &lt;sup&gt;⁎&lt;/sup&gt;-isomorphism, and &lt;em&gt;β&lt;/em&gt; is a &lt;sup&gt;⁎&lt;/sup&gt;-symmetric mapping too.&lt;/div&gt;&lt;div&gt;In case that &lt;span&gt;&lt;math&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is a JBW&lt;sup&gt;⁎&lt;/sup&gt;-algebra admitting no central summands of type &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, we also address the problem of describing the form of all symmetric bilinear mappings &lt;span&gt;&lt;m","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129796"},"PeriodicalIF":1.2,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322872","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":"On the Meixner–Pollaczek polynomials and the Sturm–Liouville problems","authors":"Mourad E.H. Ismail ,&nbsp;Nasser Saad","doi":"10.1016/j.jmaa.2025.129794","DOIUrl":"10.1016/j.jmaa.2025.129794","url":null,"abstract":"<div><div>This work provides a detailed study of Meixner–Pollaczek polynomials and employs the central difference operator to study the Sturm–Liouville problem. It presents two linearly independent solutions to the recursion relation, along with the associated difference equations. Additionally, the establishment of second-kind functions is discussed.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129794"},"PeriodicalIF":1.2,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291577","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}