Analysis and Mathematical Physics最新文献_第7页

A fractional de Rham complex for coframe-attached Maxwell equations 坐标系附加麦克斯韦方程组的分数de Rham复形

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-23 DOI: 10.1007/s13324-026-01248-w

Marvin Fritz

{"title":"A fractional de Rham complex for coframe-attached Maxwell equations","authors":"Marvin Fritz","doi":"10.1007/s13324-026-01248-w","DOIUrl":"10.1007/s13324-026-01248-w","url":null,"abstract":"<div><p>We develop a coordinate-anchored pointwise theory of fractional tangent functionals on bounded rectangles. By working on the range of the coordinatewise Riemann–Liouville integral, we define anchored fractional operators by exact inversion and prove a representation theorem: every coordinate fractional tangent functional is a scalar multiple of evaluation of the inverse operator at the base point, and the normalized one is unique. At interior points, the resulting fractional tangent space acts faithfully on the common anchored space. We then construct an exterior algebra over the polynomial algebra generated by the fractional coordinate primitives. Its fractional exterior differential defines a nilpotent algebraic chain complex, admits an explicit polynomial Poincaré homotopy, and is related to the ordinary polynomial de Rham complex by a positive diagonal rescaling. Since this fractional differential is not a graded derivation for the ordinary wedge product, the global object is a de Rham-type chain complex. We also prove a rigidity theorem for positive-cone-preserving linear coordinate changes preserving the fractional coframe and formulate a Lorentzian coframe-attached Maxwell-type system, deriving charge conservation and fractional wave equations within the polynomial coefficient class.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01248-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614077","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

On mappings with a bounded Dirichlet integral 关于有界狄利克雷积分的映射

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-20 DOI: 10.1007/s13324-026-01247-x

Mihai Cristea

引用次数: 0

Weyl quantization of exponential lie groups for square integrable representations 平方可积表示的指数李群的Weyl量化

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-16 DOI: 10.1007/s13324-026-01234-2

Stine Marie Berge, Simon Halvdansson

{"title":"Weyl quantization of exponential lie groups for square integrable representations","authors":"Stine Marie Berge, Simon Halvdansson","doi":"10.1007/s13324-026-01234-2","DOIUrl":"10.1007/s13324-026-01234-2","url":null,"abstract":"<div><p>We construct a general quantization procedure for square integrable functions on well-behaved connected exponential Lie groups. The Lie groups in question will act as the phase space, and should admit at least one open co-adjoint orbit in the topology of <span>(mathfrak {g}^*)</span>. The construction is based on composing the Fourier-Wigner transform with another Fourier transform we call the Fourier-Kirillov transform. This quantization has many desirable properties including respecting function translations, inducing an isomorphism from square integrable functions to Hilbert-Schmidt operators, and inducing a well-behaved Wigner distribution. Moreover, we investigate the connection to the operator convolutions of quantum harmonic analysis. This is intricately connected to Weyl quantization in the Weyl-Heisenberg setting. We find that convolution relations in quantum harmonic analysis can be written as group convolutions of Weyl quantizations. This implies that the squared modulus of the wavelet transform of the representation can be written as a convolution between two Wigner distributions. Lastly, we look at how we can extend known results based on Weyl quantization to wider classes of groups using our quantization procedure.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-026-01234-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466494","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

From hyperbolic to complex Euler integrals 从双曲积分到复欧拉积分

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1007/s13324-026-01238-y

N. M. Belousov, G. A. Sarkissian, V. P. Spiridonov

引用次数: 0

Embedding of (F_{log }(p,p-2,s)) into Tent spaces and Volterra integral operators 将(F_{log }(p,p-2,s))嵌入帐篷空间和Volterra积分算子

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1007/s13324-026-01243-1

Qinghua Hu, Ding Nan, Xiangling Zhu

引用次数: 0

Integrability from supersymmetric duality: a short review 超对称对偶的可积性：一个简短的回顾

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1007/s13324-026-01224-4

Ilmar Gahramanov

引用次数: 0

Effective dynamics for a class of stochastic parabolic equations with a fast oscillation driven by fractional Brownian motion and Poisson jumps 一类由分数阶布朗运动和泊松跳驱动的快速振荡随机抛物方程的有效动力学

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-14 DOI: 10.1007/s13324-026-01244-0

Jin-wei Zhao, Bin Ge, Lu Liu

引用次数: 0

Quantum Integral Inequalities: Newton and Ostrowski Approaches in Electrical, Chemical, and Optimal Systems 量子积分不等式：电学、化学和最优系统中的牛顿和奥斯特洛夫斯基方法

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-13 DOI: 10.1007/s13324-026-01239-x

Wen-li Wang, Ahsan Fareed Shah, Salah Mahmoud Boulaaras, Muhammad Shoaib Saleem

引用次数: 0

The nonlinear Steklov problem in outward cuspidal domains 外斜域中的非线性Steklov问题

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-11 DOI: 10.1007/s13324-026-01241-3

Pier Domenico Lamberti, Alexander Ukhlov

引用次数: 0

Cartan geometries with model the future lightlike cone of Lorentz-Minkowski spacetime 用卡坦几何模型来模拟洛伦兹-闵可夫斯基时空的未来光锥

IF 1.3 3区数学

Analysis and Mathematical Physics Pub Date : 2026-07-10 DOI: 10.1007/s13324-026-01242-2

Rodrigo Morón, Francisco J. Palomo

{"title":"Cartan geometries with model the future lightlike cone of Lorentz-Minkowski spacetime","authors":"Rodrigo Morón, Francisco J. Palomo","doi":"10.1007/s13324-026-01242-2","DOIUrl":"10.1007/s13324-026-01242-2","url":null,"abstract":"<div><p>This paper develops the theory of Cartan geometries modeled on the future lightlike cone of Lorentz–Minkowski spacetime, which we refer to as lightlike Cartan geometries. We show that such geometries naturally induce on the base manifold a lightlike metric, a globally defined radical vector field, and two additional compatible structures. Within this framework, we construct the standard tractor bundle associated with a lightlike Cartan geometry, showing that it extends the tangent bundle of the base manifold and carries a canonical metric linear connection. This construction provides an alternative characterization of lightlike Cartan geometries purely in terms of vector bundle data. Using this alternative description, we analyze the additional geometric information encoded in the Cartan connection beyond the metric and radical data, and we show how it can be extracted via natural decompositions of the standard tractor bundle. Our results underscore the intrinsic significance of Cartan connection methods in the study of lightlike geometry and open new avenues for the analysis of geometric structures that are neither parabolic nor reductive.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465605","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