Journal of Mathematical Analysis and Applications最新文献

{"title":"Wiener pairs of Banach algebras of operator-valued matrices","authors":"Lukas Köhldorfer,&nbsp;Peter Balazs","doi":"10.1016/j.jmaa.2025.129525","DOIUrl":"10.1016/j.jmaa.2025.129525","url":null,"abstract":"<div><div>In this article we consider several new examples of Wiener pairs <span><math><mi>A</mi><mo>⊆</mo><mi>B</mi></math></span>, where <span><math><mi>B</mi><mo>=</mo><mi>B</mi><mo>(</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>X</mi><mo>;</mo><mi>H</mi><mo>)</mo><mo>)</mo></math></span> is the Banach algebra of bounded operators acting on the Hilbert space-valued Bochner sequence space <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>X</mi><mo>;</mo><mi>H</mi><mo>)</mo></math></span> and <span><math><mi>A</mi><mo>=</mo><mi>A</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is a Banach algebra consisting of operator-valued matrices indexed by some relatively separated set <span><math><mi>X</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. In particular, we consider <span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span>-valued versions of the Jaffard algebra, of certain weighted Schur-type algebras, of Banach algebras which are defined by more general off-diagonal decay conditions than polynomial decay, of weighted versions of the Baskakov-Gohberg-Sjöstrand algebra, and of anisotropic variations of all of these matrix algebras, and show that they are inverse-closed in <span><math><mi>B</mi><mo>(</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>X</mi><mo>;</mo><mi>H</mi><mo>)</mo><mo>)</mo></math></span>. In addition, we obtain that each of these Banach algebras is symmetric.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129525"},"PeriodicalIF":1.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768567","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":"Unique solutions to power-transformed affine systems","authors":"John Stachurski ,&nbsp;Ole Wilms ,&nbsp;Junnan Zhang","doi":"10.1016/j.jmaa.2025.129515","DOIUrl":"10.1016/j.jmaa.2025.129515","url":null,"abstract":"<div><div>Systems of the form <span><math><mi>x</mi><mo>=</mo><msup><mrow><mo>(</mo><mi>A</mi><msup><mrow><mi>x</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mi>s</mi></mrow></msup><mo>+</mo><mi>b</mi></math></span> arise in a range of economic and financial applications, where <em>A</em> is a linear operator acting on a space of real-valued functions (or vectors) and <em>s</em> is a nonzero real value. In these applications, attention is focused on positive solutions. We provide a simple characterization of existence and uniqueness of positive solutions when <em>b</em> is positive and <em>A</em> is irreducible.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129515"},"PeriodicalIF":1.2,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705439","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":"Identities for the product of two Dirichlet series satisfying Hecke's functional equation","authors":"Bruce C. Berndt,&nbsp;Likun Xie","doi":"10.1016/j.jmaa.2025.129514","DOIUrl":"10.1016/j.jmaa.2025.129514","url":null,"abstract":"<div><div>We derive a general formula for the product of two Dirichlet series that satisfy Hecke's functional equation. Several examples are provided to demonstrate the applicability of the formula. In addition, we discuss prior work on similar products and clarify certain issues arising in the existing literature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129514"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739757","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":"Riesz transforms for bi-Schrödinger operators on weighted Lebesgue spaces","authors":"Nguyen Ngoc Trong ,&nbsp;Le Xuan Truong ,&nbsp;Tan Duc Do","doi":"10.1016/j.jmaa.2025.129516","DOIUrl":"10.1016/j.jmaa.2025.129516","url":null,"abstract":"<div><div>Let <span><math><mi>d</mi><mo>∈</mo><mo>{</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>…</mo><mo>}</mo></math></span> and a weight <span><math><mi>w</mi><mo>∈</mo><msubsup><mrow><mi>A</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>ρ</mi></mrow></msubsup></math></span>. We consider the fourth-order Riesz transform <span><math><mi>T</mi><mo>=</mo><msup><mrow><mi>∇</mi></mrow><mrow><mn>4</mn></mrow></msup><mspace></mspace><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> associated with the bi-Schrödinger operator <span><math><mi>L</mi><mo>=</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <span><math><mi>V</mi><mo>∈</mo><mi>R</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>σ</mi></mrow></msub><mo>∩</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> with <span><math><mi>σ</mi><mo>&gt;</mo><mfrac><mrow><mn>2</mn><mi>d</mi></mrow><mrow><mn>3</mn></mrow></mfrac></math></span> and <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> stands for a Gaussian class of potentials. We show that <em>T</em> is bounded on <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>w</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> for all <em>p</em> in a suitable range depending on <em>σ</em>. If more conditions are imposed on either <em>σ</em> or <em>V</em>, the range for <em>p</em> can be extended to <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129516"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697914","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 asymptotics of oscillatory solutions to nth-order delay differential equations","authors":"Elena Braverman ,&nbsp;Alexander Domoshnitsky ,&nbsp;John Ioannis Stavroulakis","doi":"10.1016/j.jmaa.2025.129507","DOIUrl":"10.1016/j.jmaa.2025.129507","url":null,"abstract":"<div><div>We study bounded and decaying to zero solutions of the delay differential equation<span><span><span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>+</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></munderover><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mi>x</mi><mo>(</mo><mi>t</mi><mo>−</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo><mo>=</mo><mn>0</mn><mspace></mspace><mtext>for</mtext><mspace></mspace><mi>t</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>(</mo><mi>ξ</mi><mo>)</mo><mo>=</mo><mi>φ</mi><mo>(</mo><mi>ξ</mi><mo>)</mo><mspace></mspace><mtext>for </mtext><mspace></mspace><mi>ξ</mi><mo>&lt;</mo><mn>0</mn><mo>.</mo></math></span></span></span> Kondrat'ev and Kiguradze introduced and defined principles of asymptotic behavior for its solution in the sense of the trichotomy: oscillatory, non-oscillatory with absolute values monotonically decaying to zero or monotonically increasing to ∞. Expanding upon such studies, we estimate the oscillation amplitudes of solutions. Decay to zero is established through fast oscillation: once distances between zeros are small enough, the Grönwall inequality growth estimate implies the amplitudes decrease to zero as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>. Exact growth estimates and calculation of these distances between zeros are proposed through evaluation for the spectral radii of some compact operators associated with the Green's function for an <em>n</em>-point problem.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129507"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739612","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":"Global dynamics of Liénard systems with arbitrary degrees","authors":"Hebai Chen,&nbsp;Zhijie Li,&nbsp;Yu Xiao,&nbsp;Xin Yang","doi":"10.1016/j.jmaa.2025.129503","DOIUrl":"10.1016/j.jmaa.2025.129503","url":null,"abstract":"<div><div>The aim of this paper is to study global dynamics of Liénard systems with arbitrary degrees <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><mi>y</mi></math></span>, <span><math><mover><mrow><mi>y</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>x</mi><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>4</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo><mi>y</mi></math></span>. The complex and rich dynamics are presented, in particular, including double limit cycle bifurcation, Hopf bifurcation, homoclinic bifurcation and heteroclinic bifurcation. We illustrate theoretical results by numerical simulations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129503"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705437","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":"Composition of locally solid convergences","authors":"Eugene Bilokopytov","doi":"10.1016/j.jmaa.2025.129511","DOIUrl":"10.1016/j.jmaa.2025.129511","url":null,"abstract":"<div><div>We carry on a more detailed investigation of the composition of locally solid convergences as introduced in <span><span>[6]</span></span>, as well as the corresponding notion of idempotency considered in <span><span>[4]</span></span>. In particular, we study the interactions between these two concepts and various operations with convergences. We prove associativity of the composition and show that the adherence of an ideal with respect to an idempotent convergence is equal to its closure. Some results from <span><span>[12]</span></span> about unbounded modification of locally solid topologies are generalized to the level of locally solid idempotent convergences. A simple application of the composition allows us to answer a question from <span><span>[6]</span></span> about minimal Hausdorff locally solid convergences. We also show that the weakest Hausdorff locally solid convergence exists on an Archimedean vector lattice if and only if it is atomic.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129511"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704573","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":"Discretization theorems for entire functions of exponential type","authors":"Michael I. Ganzburg","doi":"10.1016/j.jmaa.2025.129510","DOIUrl":"10.1016/j.jmaa.2025.129510","url":null,"abstract":"<div><div>We prove <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></math></span>–discretization inequalities for entire functions <em>f</em> of exponential type in the form<span><span><span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow></msub><mo>≤</mo><msup><mrow><mo>(</mo><munderover><mo>∑</mo><mrow><mi>ν</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></munderover><msup><mrow><mo>|</mo><mi>f</mi><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>)</mo></mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mi>q</mi></mrow></msup><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow></msub><mo>,</mo><mspace></mspace><mi>q</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo><mo>,</mo></mrow></math></span></span></span> with estimates for <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. We find a necessary and sufficient condition on <span><math><mi>Ω</mi><mo>=</mo><msubsup><mrow><mo>{</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>}</mo></mrow><mrow><mi>ν</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> for the right inequality to be valid and a sufficient condition on Ω for the left one to hold true. In addition, <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>(</mo><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>b</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>)</mo></math></span>-discretization inequalities on an <em>m</em>-dimensional cube are proved for entire functions of exponential type and exponential polynomials.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129510"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739774","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":"Global well-posedness for the Cauchy problem of a system of convection–diffusion equations in the critical uniformly local space","authors":"Md. Rabiul Haque ,&nbsp;Takayoshi Ogawa ,&nbsp;Atsuko Okada","doi":"10.1016/j.jmaa.2025.129508","DOIUrl":"10.1016/j.jmaa.2025.129508","url":null,"abstract":"<div><div>We establish the time global well-posedness of the Cauchy problem for a convection–diffusion system of diagonal type in uniformly local Lebesgue spaces <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>uloc</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>;</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></math></span>. Our well-posedness result also demonstrates the existence of almost periodic solutions or non-zero asymptotic boundary conditions within the functional analytic framework, extending the scalar case presented in <span><span>[18]</span></span>. For local well-posedness, we apply uniformly local <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>uloc</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>- <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>uloc</mi></mrow><mrow><mi>q</mi></mrow></msubsup></math></span> estimate for the heat evolution operator and the Banach-Caccioppoli fixed point theorem, following the approach in <span><span>[18]</span></span>. The time global well-posedness of the system, including the scaling critical case, is established by demonstrating that the solution of a single equation derived from the system satisfies a uniform bounded estimate, despite the absence of conservation laws. The proof is based on the Bernstein type argument for deriving the global a priori estimate (cf. <span><span>[19]</span></span>).</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129508"},"PeriodicalIF":1.2,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807635","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":"Inversion of the two-data spherical Radon transform with the centers on a plane","authors":"Rafik Aramyan","doi":"10.1016/j.jmaa.2025.129512","DOIUrl":"10.1016/j.jmaa.2025.129512","url":null,"abstract":"<div><div>Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. It is possible to reconstruct a function compactly supported on one side of a hyperplane using SRT over spheres centered on the hyperplane. In this article, for the reconstruction of <span><math><mi>f</mi><mo>∈</mo><mi>C</mi><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> (the support can be non-compact) using SRT over spheres centered on a plane, an additional condition is found, which is a weighted SRT (to reconstruct an odd function with respect to the hyperplane), and the injectivity of the so-called two data spherical Radon transform is considered. The transform consists of the classical SRT and the weighted SRT. An inversion formula of the transform that uses the local data of the spherical integrals to reconstruct the unknown function is presented. The inversion formula generalizes the inversion formula of SRT for functions supported on one side of a plane, as obtained earlier by the author of this article. Such inversions have theoretical significance in many areas of mathematics and are the mathematical base of modern modalities of imaging, such as Thermo and photoacoustic tomography, radar imaging, geophysics, and a few others.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129512"},"PeriodicalIF":1.2,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143724058","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}