Journal of Mathematical Analysis and Applications最新文献

{"title":"On accumulated spectrograms for Gabor frames","authors":"Simon Halvdansson","doi":"10.1016/j.jmaa.2024.129044","DOIUrl":"10.1016/j.jmaa.2024.129044","url":null,"abstract":"<div><div>Analogs of classical results on accumulated spectrograms, the sum of spectrograms of eigenfunctions of localization operators, are established for Gabor multipliers. We show that the lattice <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> distance between the accumulated spectrogram and the indicator function of the Gabor multiplier mask is bounded by the number of lattice points near the boundary of the mask and that this bound is sharp in general. The methods developed for the proofs are also used to show that the Weyl-Heisenberg ensemble restricted to a lattice is hyperuniform when the Gabor frame is tight.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129044"},"PeriodicalIF":1.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Lomonosov type theorems and the invariant subspace problem for non-archimedean Banach spaces","authors":"A. El Asri ,&nbsp;A. Kubzdela ,&nbsp;M. Babahmed","doi":"10.1016/j.jmaa.2024.129043","DOIUrl":"10.1016/j.jmaa.2024.129043","url":null,"abstract":"<div><div>In this paper, we study the existence of invariant (and even hyperinvariant) subspaces of bounded operators on a non-archimedean Banach space <span><math><mi>E</mi><mo>=</mo><mo>(</mo><mi>E</mi><mo>,</mo><mo>‖</mo><mo>.</mo><mo>‖</mo><mo>)</mo></math></span> over a valued field <span><math><mi>K</mi></math></span> equipped with a non-trivial non-archimedean valuation <span><math><mo>|</mo><mo>.</mo><mo>|</mo></math></span>. Specifically, we consider compact operators and operators that commute with a compact operator. First we show that if <strong>E</strong> has a base, then any compact operator <strong>T</strong> such that <span><math><msub><mrow><mi>lim</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>⁡</mo><msup><mrow><mo>‖</mo><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>‖</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup><mo>&gt;</mo><mn>0</mn></math></span> has a finite-dimensional hyperinvariant subspace. Next we show that if <span><math><mi>K</mi></math></span> is locally compact, then every compact operator <strong>T</strong> on <strong>E</strong> has a hyperinvariant subspace. Afterward, assuming that <span><math><mi>K</mi></math></span> is spherically complete or <strong>E</strong> is of countable type, we provide a necessary condition for a bounded operator on <strong>E</strong> to have a hyperinvariant subspace. We demonstrate that the classical Lomonosov Invariant Subspace theorem does not hold in the case where <span><math><mi>K</mi></math></span> is non-spherically complete. Finally, we prove Lomonosov type theorem for spectral quasinilpotent operators, when <span><math><mi>K</mi></math></span> is locally compact.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129043"},"PeriodicalIF":1.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656132","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":"Band projections and order idempotents in Banach lattice algebras","authors":"David Muñoz-Lahoz","doi":"10.1016/j.jmaa.2024.129045","DOIUrl":"10.1016/j.jmaa.2024.129045","url":null,"abstract":"<div><div>Motivated by recent work about band projections on spaces of regular operators over a Banach lattice, given a Banach lattice algebra <em>A</em>, we will say an element <span><math><mi>a</mi><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> is a band projection if the multiplication operator <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>a</mi></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is a band projection. Our aim in this note is to explore the relations between this and the notion of order idempotent (those elements <em>a</em> in a Banach lattice algebra <em>A</em> with identity <em>e</em> such that <span><math><mn>0</mn><mo>≤</mo><mi>a</mi><mo>≤</mo><mi>e</mi></math></span> and <span><math><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mi>a</mi></math></span>). We also revisit the properties of the ideal generated by the identity on a Banach lattice algebra, motivated by those of the centre of a Banach lattice.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129045"},"PeriodicalIF":1.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Banaś modulus of smoothness and Gao Pythagorean constant of Lp(μ)","authors":"Alireza Amini-Harandi,&nbsp;Malihe Peyvaste","doi":"10.1016/j.jmaa.2024.129046","DOIUrl":"10.1016/j.jmaa.2024.129046","url":null,"abstract":"<div><div>In this paper, we first compute the Banaś modulus of smoothness of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, which gives a solution to the problem posed by Banaś in 1986 (see Problem 4 of Banas (1986) <span><span>[1]</span></span>). Then, we introduce and calculate Gao Pythagorean constant of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, which extends and improves some main results of Gao (2006) <span><span>[3]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129046"},"PeriodicalIF":1.2,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656130","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":"Long time stability of fractional nonlinear Schrödinger equations","authors":"Xue Yang,&nbsp;Jing Zhang,&nbsp;Jieyu Liu","doi":"10.1016/j.jmaa.2024.129035","DOIUrl":"10.1016/j.jmaa.2024.129035","url":null,"abstract":"<div><div>We investigate the long time stability of the solutions to the fractional nonlinear Schrödinger (FNLS) equation under periodic boundary condition<span><span><span><math><mi>i</mi><msub><mrow><mi>ψ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msup><mi>ψ</mi><mo>+</mo><mfrac><mrow><mo>∂</mo><mi>F</mi><mo>(</mo><mo>|</mo><mi>ψ</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>∂</mo><mover><mrow><mi>ψ</mi></mrow><mo>‾</mo></mover></mrow></mfrac><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>T</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>∈</mo><mi>R</mi><mo>,</mo><mspace></mspace><msub><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mrow><mo>(</mo><mn>3</mn><mo>/</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo></math></span></span></span> where <span><math><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msup></math></span> denotes the Riesz fractional differentiation defined in <span><span>[18]</span></span>. Here <span><math><mi>F</mi><mo>(</mo><mi>z</mi><mo>)</mo></math></span> is a real-valued polynomial function of <em>z</em>, fulfilling <span><math><msup><mrow><mi>F</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>z</mi><mo>)</mo><msub><mrow><mo>|</mo></mrow><mrow><mi>z</mi><mo>=</mo><mn>0</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span>, <span><math><msup><mrow><mi>F</mi></mrow><mrow><mo>″</mo></mrow></msup><mo>(</mo><mi>z</mi><mo>)</mo><msub><mrow><mo>|</mo></mrow><mrow><mi>z</mi><mo>=</mo><mn>0</mn></mrow></msub><mo>≠</mo><mn>0</mn></math></span>. Our findings indicate that for all <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mrow><mo>(</mo><mn>3</mn><mo>/</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> and almost all <em>R</em>-small initial data in Sobolev norm, the corresponding solutions remain their small magnitude over time-intervals of length <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>−</mo><mo>|</mo><mi>ln</mi><mo>⁡</mo><mi>R</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>γ</mi></mrow></msup></mrow></msup></math></span> with <span><math><mn>0</mn><mo>&lt;</mo><mi>R</mi><mo>≪</mo><mn>1</mn></math></span>, <span><math><mn>0</mn><mo>&lt;</mo><mi>γ</mi><mo>&lt;</mo><mn>1</mn><mo>/</mo><mn>5</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129035"},"PeriodicalIF":1.2,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747092","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":"Shape reconstruction of a cavity with impedance boundary condition via the reciprocity gap method","authors":"Xueping Chen,&nbsp;Yuan Li","doi":"10.1016/j.jmaa.2024.129034","DOIUrl":"10.1016/j.jmaa.2024.129034","url":null,"abstract":"<div><div>We consider an interior inverse scattering problem of reconstructing the shape of a cavity with impedance boundary condition from measured Cauchy data of the total field. The incident point sources and the measurements are distributed on two different manifolds inside the cavity. We first prove that the boundary of the cavity and the surface impedance can be uniquely determined by the scattered field data on the measurement manifold. Then we develop a reciprocity gap (RG) method to reconstruct the cavity. The theoretical analysis shows the uniquely solvability and existence of the approximate solution for the linear integral equation constructed in the RG method. We also prove that the shape of the cavity can be characterized by the blow-up property of the approximate solution of the proposed integral equation. Numerical examples are presented to verify the feasibility of the RG method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129034"},"PeriodicalIF":1.2,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656127","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":"Asymptotic approximations for the distribution of the product of correlated normal random variables","authors":"Robert E. Gaunt,&nbsp;Zixin Ye","doi":"10.1016/j.jmaa.2024.128987","DOIUrl":"10.1016/j.jmaa.2024.128987","url":null,"abstract":"<div><div>We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the tail probabilities and quantile functions of this distribution, as well as an asymptotic approximation for the widely used risk measures value at risk and tail value at risk.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128987"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Error estimates for the robust α-stable central limit theorem under sublinear expectation by a discrete approximation method","authors":"Lianzi Jiang","doi":"10.1016/j.jmaa.2024.129028","DOIUrl":"10.1016/j.jmaa.2024.129028","url":null,"abstract":"<div><div>In this work, we develop a numerical method to study the error estimates of the <em>α</em>-stable central limit theorem under sublinear expectation with <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, whose limit distribution can be characterized by a fully nonlinear integro-differential equation (PIDE). Based on the sequence of independent random variables, we propose a discrete approximation scheme for the fully nonlinear PIDE. With the help of the nonlinear stochastic analysis techniques and numerical analysis tools, we establish the error bounds for the discrete approximation scheme, which in turn provides a general error bound for the robust <em>α</em>-stable central limit theorem, including the integrable case <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> as well as the non-integrable case <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. Finally, we provide some concrete examples to illustrate our main results and derive the precise convergence rates.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129028"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593041","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":"Higher-order fractional equations and related time-changed pseudo-processes","authors":"Fabrizio Cinque,&nbsp;Enzo Orsingher","doi":"10.1016/j.jmaa.2024.129026","DOIUrl":"10.1016/j.jmaa.2024.129026","url":null,"abstract":"<div><div>We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of “stochastic composition” of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce stable pseudo-subordinators as well as their pseudo-inverses. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and their inverse processes.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129026"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656119","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 reduced-dimension method of Crank-Nicolson finite element solution coefficient vectors for the unsteady Burgers equation","authors":"Chunxia Huang,&nbsp;Hong Li,&nbsp;Baoli Yin","doi":"10.1016/j.jmaa.2024.129031","DOIUrl":"10.1016/j.jmaa.2024.129031","url":null,"abstract":"<div><div>This paper primarily focuses on the dimensionality reduction of finite element (FE) solution coefficient vectors for the unsteady Burgers equation, solved using the Crank-Nicolson FE (CNFE) method. The proper orthogonal decomposition (POD) basis is constructed from the snapshot matrix, which is formed using the first <em>L</em> solutions, where <em>L</em> is significantly smaller than the total number of time steps <em>N</em> of the CNFE method. By reconstructing the matrix form of the CNFE method, a reduced-dimension Crank-Nicolson finite element (RDCNFE) method is proposed and stability analysis and error estimates are discussed. Numerical tests are implemented to verify the theoretical results and demonstrate the high efficiency of the RDCNFE method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129031"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656120","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}