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Elements (functions) that are universal with respect to a minimal system 相对于最小系统来说是通用的元素（函数）
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-14 DOI: 10.1007/s13324-026-01268-6
Zhirayr Avetisyan, Martin Grigoryan, Michael Ruzhansky
{"title":"Elements (functions) that are universal with respect to a minimal system","authors":"Zhirayr Avetisyan,&nbsp;Martin Grigoryan,&nbsp;Michael Ruzhansky","doi":"10.1007/s13324-026-01268-6","DOIUrl":"10.1007/s13324-026-01268-6","url":null,"abstract":"<div><p>We call an element <i>U</i> conditionally universal for a sequential convergence space <span>(mathbf {Omega })</span> with respect to a minimal system <span>({varphi _n}_{n=1}^infty )</span> in a continuously and densely embedded Banach space <span>(mathcal {X}hookrightarrow mathbf {Omega })</span> if the partial sums of its phase-modified Fourier series is dense in <span>(mathbf {Omega })</span>. We will call the element <i>U</i> almost universal if the change of phases (signs) needs to be performed only on a thin subset of Fourier coefficients. In this paper we prove the existence of an almost universal element under certain assumptions on the system <span>({varphi _n}_{n=1}^infty )</span>. We will call a function <i>U</i> asymptotically conditionally universal in a space <span>(L^1(mathcal {M}))</span> if the partial sums of its phase-modified Fourier series is dense in <span>(L^1(F_m))</span> for an ever-growing sequence of subsets <span>(F_msubset mathcal {M})</span> with asymptotically null complement. Here we prove the existence of such functions <i>U</i> under certain assumptions on the system <span>({varphi _n}_{n=1}^infty )</span>. Moreover, we show that every integrable function can be slightly modified to yield such a function <i>U</i>. In particular, we establish the existence of almost universal functions for <span>(L^p([0,1]))</span>, <span>(pin (0,1))</span>, and asymptotically conditionally universal functions for <span>(L^1([0,1]))</span>, with respect to the trigonometric system.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986341","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}
引用次数: 0
Inversion of spherical mean transform in odd dimensions with partial data via system of ODEs 利用微分方程系统反演部分数据奇维球面平均变换
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-12 DOI: 10.1007/s13324-026-01267-7
Pradipta Chatterjee, Venkateswaran P. Krishnan, Abhilash Tushir
{"title":"Inversion of spherical mean transform in odd dimensions with partial data via system of ODEs","authors":"Pradipta Chatterjee,&nbsp;Venkateswaran P. Krishnan,&nbsp;Abhilash Tushir","doi":"10.1007/s13324-026-01267-7","DOIUrl":"10.1007/s13324-026-01267-7","url":null,"abstract":"<div><p>We derive an inversion algorithm for the spherical mean transform in odd dimensions with partial radial data. We prove that the reconstruction of the unknown function can be reduced to solving ordinary differential equations, thereby providing a more direct approach in odd dimensions than solving Volterra integral equation of the first kind established in prior works. We also provide analytical solutions in some special cases. Our work answers a question posed by Rubin in [38].</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927431","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}
引用次数: 0
Inversion of spherical mean transform in odd dimensions with partial data via system of ODEs 利用微分方程系统反演部分数据奇维球面平均变换
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-12 DOI: 10.1007/s13324-026-01267-7
Pradipta Chatterjee, Venkateswaran P. Krishnan, Abhilash Tushir
{"title":"Inversion of spherical mean transform in odd dimensions with partial data via system of ODEs","authors":"Pradipta Chatterjee,&nbsp;Venkateswaran P. Krishnan,&nbsp;Abhilash Tushir","doi":"10.1007/s13324-026-01267-7","DOIUrl":"10.1007/s13324-026-01267-7","url":null,"abstract":"<div><p>We derive an inversion algorithm for the spherical mean transform in odd dimensions with partial radial data. We prove that the reconstruction of the unknown function can be reduced to solving ordinary differential equations, thereby providing a more direct approach in odd dimensions than solving Volterra integral equation of the first kind established in prior works. We also provide analytical solutions in some special cases. Our work answers a question posed by Rubin in [38].</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927435","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}
引用次数: 0
Lévy Laplacian on manifold and heat flows of differential forms 流形和微分形式热流的拉普拉斯变换
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-10 DOI: 10.1007/s13324-026-01269-5
Boris Volkov
{"title":"Lévy Laplacian on manifold and heat flows of differential forms","authors":"Boris Volkov","doi":"10.1007/s13324-026-01269-5","DOIUrl":"10.1007/s13324-026-01269-5","url":null,"abstract":"<div><p>The Lévy Laplacian is an infinite-dimensional differential operator that is of interest due to its connection with the Yang–Mills gauge fields. This paper proves that three different definitions of the Lévy Laplacian on the manifold of <span>(H^1)</span>-paths on a Riemannian manifold coincide on their common domain. The heat equation with the Lévy Laplacian is considered. It is shown that some solutions of this heat equation converge as time tends to infinity to functionals that are constant on homotopy equivalent curves. These solutions are constructed using heat flows of differential 0-forms and 1-forms on the compact Riemannian manifold.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927446","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}
引用次数: 0
A stochastic Schauder-Tychonoff type theorem and its applications 一个随机Schauder-Tychonoff型定理及其应用
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-10 DOI: 10.1007/s13324-026-01262-y
Erika Hausenblas, Ankit Kumar, Jonas M. Tölle
{"title":"A stochastic Schauder-Tychonoff type theorem and its applications","authors":"Erika Hausenblas,&nbsp;Ankit Kumar,&nbsp;Jonas M. Tölle","doi":"10.1007/s13324-026-01262-y","DOIUrl":"10.1007/s13324-026-01262-y","url":null,"abstract":"<div><p>One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our existence result to nonlinear stochastic diffusion equations with non-Lipschitz perturbations.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01262-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927445","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}
引用次数: 0
Lévy Laplacian on manifold and heat flows of differential forms 流形和微分形式热流的拉普拉斯变换
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-10 DOI: 10.1007/s13324-026-01269-5
Boris Volkov
{"title":"Lévy Laplacian on manifold and heat flows of differential forms","authors":"Boris Volkov","doi":"10.1007/s13324-026-01269-5","DOIUrl":"10.1007/s13324-026-01269-5","url":null,"abstract":"<div><p>The Lévy Laplacian is an infinite-dimensional differential operator that is of interest due to its connection with the Yang–Mills gauge fields. This paper proves that three different definitions of the Lévy Laplacian on the manifold of <span>(H^1)</span>-paths on a Riemannian manifold coincide on their common domain. The heat equation with the Lévy Laplacian is considered. It is shown that some solutions of this heat equation converge as time tends to infinity to functionals that are constant on homotopy equivalent curves. These solutions are constructed using heat flows of differential 0-forms and 1-forms on the compact Riemannian manifold.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927362","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}
引用次数: 0
A stochastic Schauder-Tychonoff type theorem and its applications 一个随机Schauder-Tychonoff型定理及其应用
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-10 DOI: 10.1007/s13324-026-01262-y
Erika Hausenblas, Ankit Kumar, Jonas M. Tölle
{"title":"A stochastic Schauder-Tychonoff type theorem and its applications","authors":"Erika Hausenblas,&nbsp;Ankit Kumar,&nbsp;Jonas M. Tölle","doi":"10.1007/s13324-026-01262-y","DOIUrl":"10.1007/s13324-026-01262-y","url":null,"abstract":"<div><p>One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our existence result to nonlinear stochastic diffusion equations with non-Lipschitz perturbations.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01262-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927361","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}
引用次数: 0
Order-spectrum preserving maps on unbounded operators 无界算子上的保序谱映射
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-04 DOI: 10.1007/s13324-026-01266-8
Youssef El Khatiri
{"title":"Order-spectrum preserving maps on unbounded operators","authors":"Youssef El Khatiri","doi":"10.1007/s13324-026-01266-8","DOIUrl":"10.1007/s13324-026-01266-8","url":null,"abstract":"<div><p>We classify surjective maps that preserve both order and spectrum on positive unbounded self-adjoint operators. As a consequence, we provide a comprehensive description of such maps on the set of all lower semi-bounded self-adjoint operators.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926361","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}
引用次数: 0
Order-spectrum preserving maps on unbounded operators 无界算子上的保序谱映射
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-04 DOI: 10.1007/s13324-026-01266-8
Youssef El Khatiri
{"title":"Order-spectrum preserving maps on unbounded operators","authors":"Youssef El Khatiri","doi":"10.1007/s13324-026-01266-8","DOIUrl":"10.1007/s13324-026-01266-8","url":null,"abstract":"<div><p>We classify surjective maps that preserve both order and spectrum on positive unbounded self-adjoint operators. As a consequence, we provide a comprehensive description of such maps on the set of all lower semi-bounded self-adjoint operators.\u0000</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926360","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}
引用次数: 0
Asymptotic expansions for semilinear waves on asymptotically flat spacetimes 渐近平坦时空上半线性波的渐近展开式
IF 1.3 3区 数学
Analysis and Mathematical Physics Pub Date : 2026-09-01 DOI: 10.1007/s13324-026-01264-w
Sam Looi, Haoren Xiong
{"title":"Asymptotic expansions for semilinear waves on asymptotically flat spacetimes","authors":"Sam Looi,&nbsp;Haoren Xiong","doi":"10.1007/s13324-026-01264-w","DOIUrl":"10.1007/s13324-026-01264-w","url":null,"abstract":"<div><p>We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. Our analysis focuses on two key cases: cubic nonlinearities and higher-order power nonlinearities. For cubic nonlinearities of the form <span>(a(t,x) , phi ^3)</span>, we prove asymptotic expansions for the solution globally in the spacetime. In the special case of compact spatial regions, solutions exhibit the asymptotic behavior <span>(phi (t, x) = c , t^{-2} + mathcal {O}(t^{-3+}))</span>. For higher-order nonlinearities <span>(a(t,x) , phi ^p)</span> with <span>(p ge 4)</span>, we prove the solution satisfies <span>(phi (t, x) = d , t^{-3} + mathcal {O}(t^{-4+}))</span>, thereby extending the classical Price’s law (a late-time tail postulated in 1972) to nonlinear settings in a precise fashion. These results sharpen previous decay estimates for nonlinear waves. We develop a radiation field expansion and a low-energy resolvent expansion adapted to conormal asymptotic inputs, extending Hintz’s approach for linear waves to the semilinear setting. Our methods connect geometric microlocal analysis (b-calculus) with classical physical-space techniques, providing a convenient tool for analyzing asymptotic behavior of nonlinear waves.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01264-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926686","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}
引用次数: 0
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