Analysis and Mathematical Physics最新文献

Octonionic dunkl transform: definition, properties, and uncertainty principles 八元离子邓克尔变换：定义、性质和测不准原理

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-05-08 DOI: 10.1007/s13324-026-01207-5

A. Achak, O. Ahmad, El. Loualid, N. Safouane

{"title":"Octonionic dunkl transform: definition, properties, and uncertainty principles","authors":"A. Achak, O. Ahmad, El. Loualid, N. Safouane","doi":"10.1007/s13324-026-01207-5","DOIUrl":"10.1007/s13324-026-01207-5","url":null,"abstract":"<div>The Dunkl transform generalizes the classical Fourier transform in the context of finite reflection groups, introducing a family of operators parameterized by a multiplicity function (textbf{k} ge 0). Hypercomplex extensions of integral transforms, particularly based on quaternion and octonion algebras, have gained prominence for processing multi-dimensional signals. In this paper, we introduce the Octonionic Dunkl Transform (ODT), which unifies the algebraic structure of the octonions—the largest normed division algebra—with the analytic framework of Dunkl operators. We provide its explicit definition, accounting for the non-associative nature of octonion multiplication through a fixed left-nested parenthesization convention. Fundamental properties are established, including linearity, a Bessel function series representation, and a detailed parity decomposition that separates the transform into eight real-valued components. We prove a sharp inversion formula and an isometry (Plancherel theorem) in the associated weighted (L^2) space. Furthermore, we establish two uncertainty principles: a Heisenberg-type inequality relating the weighted dispersions of a signal and its transform, and a Donoho-Stark-type concentration principle. These results extend earlier work on the quaternion Dunkl transform and the octonion Fourier transform, providing a new theoretical tool for the analysis of octonion-valued signals in settings with reflection symmetry.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147830061","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

Normalized positive solutions to nonhomogeneous Schrödinger-Poisson-Slater system 非齐次Schrödinger-Poisson-Slater系统的归一化正解

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-04-18 DOI: 10.1007/s13324-026-01197-4

Liping Xu, Shuangshuang Qiu

{"title":"Normalized positive solutions to nonhomogeneous Schrödinger-Poisson-Slater system","authors":"Liping Xu, Shuangshuang Qiu","doi":"10.1007/s13324-026-01197-4","DOIUrl":"10.1007/s13324-026-01197-4","url":null,"abstract":"<div>In this paper, we consider the existence of normalized positive solutions for the following nonhomogeneous Schrödinger-Poisson-Slater system <div><div>$$begin{aligned} left{ begin{array}{l} - Delta u + lambda u + left( {{{left| x right| }^{ - 1}}*{{left| u right| }^2}} right) u = fleft( u right) + hleft( x right) ,~u>0,quad in;{mathbb {R}^3}, int _{{mathbb {R}^3}} {{{left| u right| }^2}dx} = m, u in H^1(mathbb {R}^3), end{array} right. end{aligned}$$</div></div>where the frequency (lambda ) is not fixed and instead appears as a Lagrange multiplier, (m>0) is prescribed, and h(x) is a perturbation. For the case where the nonlinearity f is mass subcritical and purely power-type, we establish the existence of a normalized positive ground state under the assumption that the perturbation h(x) meets certain mild conditions. Conversely, when the nonlinearity f is mass supercritical, we demonstrate the existence of a normalized mountain pass positive solution using variational methods, provided that h(x) is a radially symmetric positive function. This appears to be the first contribution addressing the normalized solutions for such a perturbed equation with a nonlocal term. Our findings may both generalize and enhance some of the recent results found in the literature.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738237","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

On series solutions of modified Euler equations for two-dimensional incompressible irrotational flow 二维不可压缩无旋流修正欧拉方程的级数解

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-04-13 DOI: 10.1007/s13324-026-01166-x

Vesselin Vatchev

引用次数: 0

Direct spectral problems for Paley-Wiener canonical systems Paley-Wiener正则系统的直接谱问题

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-04-09 DOI: 10.1007/s13324-026-01196-5

Ashley R. Zhang

引用次数: 0

One reduction of the modified Toda hierarchy 修改后的Toda层次结构的一个简化

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-04-08 DOI: 10.1007/s13324-026-01195-6

Jinbiao Wang, Wenchuang Guan, Mengyao Chen, Jipeng Cheng

引用次数: 0

The Schwarz function and the shrinking of the Szegő curve: electrostatic, hydrodynamic, and random matrix models 施瓦兹函数和塞格格曲线的收缩：静电、流体动力和随机矩阵模型

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-04-07 DOI: 10.1007/s13324-026-01194-7

Gabriel Álvarez, Luis Martínez Alonso, Elena Medina

{"title":"The Schwarz function and the shrinking of the Szegő curve: electrostatic, hydrodynamic, and random matrix models","authors":"Gabriel Álvarez, Luis Martínez Alonso, Elena Medina","doi":"10.1007/s13324-026-01194-7","DOIUrl":"10.1007/s13324-026-01194-7","url":null,"abstract":"<div>We study the deformation of the classical Szegő curve (gamma _0) given by (gamma _t = { zin mathbb {C}: |z, e^{1-z}| = e^{-t}, |z|le 1}), (tge 0) from three different viewpoints: an electrostatic equilibrium problem, the dual hydrodynamic model, and a random matrix model. The common framework underlying these models is the asymptotic distribution of zeros of the scaled varying Laguerre polynomials (L^{(alpha _n)}_n(n z)) in the critical regime where (lim _{nrightarrow infty }alpha _n/n=-1), for which the limiting zero distribution is supported on (gamma _t), where the deformation parameter t encodes the exponential rate at which the sequence (alpha _n) approximates the set of negative integers. We show that the Schwarz functions of these curves can be written in terms of the Lambert W function, and that in this formulation the S-property of Stahl and Gonchar and Rachmanov can be explictly written as the Schwarz reflection symmetry. We also discuss a conformal map of the interior of the curves (gamma _t) onto the disks (D(0,e^{-t})) and the harmonic moments of the curves.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01194-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642825","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

A nonlinear version of Kantorovich operators with p-averages: convergence results and asymptotic formula 具有p-平均的Kantorovich算子的一个非线性版本：收敛结果和渐近公式

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-04-03 DOI: 10.1007/s13324-026-01178-7

Mirella Cappelletti Montano, Rosario Corso, Vita Leonessa

引用次数: 0

Schrödinger operators with non-integer power-law potentials and Lie-Rinehart algebras Schrödinger具有非整数幂律势和Lie-Rinehart代数的算子

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-04-03 DOI: 10.1007/s13324-026-01193-8

Ivan Beschastnyi, Catarina Carvalho, Victor Nistor, Yu Qiao

{"title":"Schrödinger operators with non-integer power-law potentials and Lie-Rinehart algebras","authors":"Ivan Beschastnyi, Catarina Carvalho, Victor Nistor, Yu Qiao","doi":"10.1007/s13324-026-01193-8","DOIUrl":"10.1007/s13324-026-01193-8","url":null,"abstract":"<div>We study Schrödinger operators (H:= -Delta + V) with potentials V that have power-law growth (not necessarily polynomial) at 0 and at (infty ) using methods of operator algebras, microlocal analysis, and Lie theory (Lie-Rinehart algebras). More precisely, we show that H is “generated” in a certain sense by an explicit Lie algebra of vector fields (a Lie-Rinehart algebra). This allows us then to construct a suitable algebra of pseudodifferential operators that yields further properties of H by using methods of operator algebras. Classically, this method was used to study H when the power-laws describing the potential V have integer exponents. Thus, the main point of this paper is that this integrality condition on the exponents is not really necessary for the approach using pseudodifferential operators and operator algebras to work. While we consider potentials following (possibly non-integer) power-laws both at the origin and at infinity, our results extend right away to potentials having power-law singularities at several points. The extension of the classical microlocal analysis and operator algebras results to potentials with non-integer power-laws is achieved by considering the setting of Lie-Rinehart algebras and of the continuous family groupoids integrating them. (The classical case relies instead on Lie algebroids and Lie groupoids.) The algebras that we construct are useful also for the study of layer potentials.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606594","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

Degenerate Mittag–Leffler functions defined via the degenerate gamma function and applications to fractional Maxwell–Zener viscoelasticity 由简并函数定义的简并Mittag-Leffler函数及其在分数阶Maxwell-Zener粘弹性中的应用

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-04-01 DOI: 10.1007/s13324-026-01189-4

Oğuz Yağcı

{"title":"Degenerate Mittag–Leffler functions defined via the degenerate gamma function and applications to fractional Maxwell–Zener viscoelasticity","authors":"Oğuz Yağcı","doi":"10.1007/s13324-026-01189-4","DOIUrl":"10.1007/s13324-026-01189-4","url":null,"abstract":"<div>Time-dependent materials often show relaxation and creep over many decades in time. Fractional Maxwell and Zener models describe this behavior with a small number of parameters, and their response functions are written in terms of Mittag–Leffler kernels. In this paper we introduce a (lambda )–deformed two-parameter Mittag–Leffler function by replacing the classical gamma denominator in the Mittag–Leffler series with the degenerate gamma function (Gamma _{lambda }). Using a Beta-integral representation of (Gamma _{lambda }), we give admissible parameters and determine the exact radius of convergence (R_{lambda }(alpha )=|lambda ^{alpha }|^{-1}), which yields a sharp disk of analyticity. We also prove that (E^{(lambda )}_{alpha ,beta }) converges to the classical Mittag–Leffler function (E_{alpha ,beta }) as (lambda rightarrow 0^{+}). A Fox–Wright representation is derived, leading to hypergeometric reductions when (alpha =1) and when (alpha in mathbb {N}). As an application, we formulate generalized fractional Maxwell and Zener viscoelastic laws in which the relaxation modulus and creep compliance are expressed through (E^{(lambda )}_{alpha ,beta }). The extra parameter (lambda ) acts as a memory-shape control that can improve fits to relaxation/creep data, while the standard fractional models are recovered in the limit (lambda rightarrow 0^{+}).</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606844","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

On links between a theorem of Schoenberg, Rohlin decompositions of measures, the Bochner-Minlos theorem and the Fock space 论Schoenberg定理、Rohlin测度分解、Bochner-Minlos定理与Fock空间的联系

IF 1.6 3区数学

Analysis and Mathematical Physics Pub Date : 2026-03-31 DOI: 10.1007/s13324-026-01190-x

Daniel Alpay, Paula Cerejeiras, Palle Jorgensen, Uwe Kaehler

{"title":"On links between a theorem of Schoenberg, Rohlin decompositions of measures, the Bochner-Minlos theorem and the Fock space","authors":"Daniel Alpay, Paula Cerejeiras, Palle Jorgensen, Uwe Kaehler","doi":"10.1007/s13324-026-01190-x","DOIUrl":"10.1007/s13324-026-01190-x","url":null,"abstract":"<div>The main goal of this paper is to gain new results in stochastics by drawing on, and combining, different areas that are normally not considered to be related. Thus, in this paper we extend the previous class of Gaussian-like functions (Mhspace{-.5mm}L) which will allow for future generalized stochastic processes in infinite dimensional analysis. We show that an approach similar to the one by the classical Bochner-Minlos theorem for the white-noise case can be achieved by using Gaussian-like functions belonging to a large family - the (Mhspace{-.5mm}L_r) classes ((0< r le infty )). We show how Schoenberg’s theorem for positive definite functions on a Hilbert space allows to go beyond the classical setting of Bochner-Milnos theorem. Furthermore, we show that the application of the Rohlin’s disintegration theorem allows for a decomposition of the associated probability measures , see Theorems 3.2 and 4.3. We end this paper with several important examples of functions in these classes (Mhspace{-.5mm}L_r) and provide some interesting counterexamples, e.g. Theorem 7.4, to get a better feeling on this classes.</div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01190-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147607082","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