Advances in Applied Clifford Algebras最新文献

Carleson Measures for Slice Regular Hardy and Bergman Spaces in Quaternions 四元数中片正则Hardy和Bergman空间的Carleson测度

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-05-26 DOI: 10.1007/s00006-025-01391-w

Wenwan Yang, Cheng Yuan

{"title":"Carleson Measures for Slice Regular Hardy and Bergman Spaces in Quaternions","authors":"Wenwan Yang, Cheng Yuan","doi":"10.1007/s00006-025-01391-w","DOIUrl":"10.1007/s00006-025-01391-w","url":null,"abstract":"<div>We study the quaternionic Carleson measure, which provides an embedding of the slice regular Hardy space ({mathcal {H}}^p({mathbb {B}})) into (L^s({mathbb {B}}, text {d}mu )) with (s>p.) A new criterion is needed for a finite positive Borel measure to be an (({mathcal {H}}^p({mathbb {B}}),s))-Carleson measure, given by the uniform integrability of slice Cauchy kernels. It turns out that the symmetric box and the symmetric pseudo-hyperbolic disc are equivalent in the characterization of (({mathcal {H}}^p({mathbb {B}}),s))-Carleson measures, while they are not when (s=p.) We further study the s-Carleson measure for slice regular Bergman spaces ({{mathcal {A}}}^p({mathbb {B}})) for all indices s, p. When (sge p,) our characterization relies on a close relation between the Carleson measure for Hardy and Bergman spaces and is primarily based on the slice Cauchy kernel, rather than the slice Bergman kernel. The advantage of the slice Cauchy kernel over the slice Bergman kernel is that, when restricted to any slice plane, the former, as a sum of two terms, transforms into a fractional linear transform, whereas the latter does not. This enables a locally uniform lower bound estimate for the slice Cauchy kernel, which is crucial in applications. In the case where (s<p,) we need to apply Khinchine’s inequality and a point-wise estimate for atoms in slice Bergman spaces based on the convex combination identity.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Rota-Baxter Operators of Nonzero Weight on the Split Octonions 分割八元上非零权的Rota-Baxter算子

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-05-24 DOI: 10.1007/s00006-025-01389-4

A. S. Panasenko

引用次数: 0

Linear Canonical Space-Time Transform and Convolution Theorems 线性正则时空变换与卷积定理

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-05-21 DOI: 10.1007/s00006-025-01386-7

Yi-Qiao Xu, Bing-Zhao Li

引用次数: 0

On Unitary Groups in Ternary and Generalized Clifford Algebras 关于三元和广义Clifford代数中的酉群

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-05-20 DOI: 10.1007/s00006-025-01388-5

Dmitry Shirokov

引用次数: 0

Introducing Multidimensional Dirac–Hestenes Equation 引入多维Dirac-Hestenes方程

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-05-09 DOI: 10.1007/s00006-025-01382-x

Sofia Rumyantseva, Dmitry Shirokov

{"title":"Introducing Multidimensional Dirac–Hestenes Equation","authors":"Sofia Rumyantseva, Dmitry Shirokov","doi":"10.1007/s00006-025-01382-x","DOIUrl":"10.1007/s00006-025-01382-x","url":null,"abstract":"<div>It is easier to investigate phenomena in particle physics geometrically by exploring a real solution to the Dirac–Hestenes equation instead of a complex solution to the Dirac equation. The current research presents a formulation of the multidimensional Dirac–Hestenes equation. Since the matrix representation of the complexified (Clifford) geometric algebra (mathbb {C}otimes C hspace{-1.00006pt}ell _{1,n}) depends on the parity of n, we examine even and odd cases separately. In the geometric algebra (C hspace{-1.00006pt}ell _{1,3}), there is a lemma on a unique decomposition of an element of the minimal left ideal into the product of the idempotent and an element of the real even subalgebra. The lemma is used to construct the four-dimensional Dirac–Hestenes equation. The analogous lemma is not valid in the multidimensional case, since the dimension of the real even subalgebra of (C hspace{-1.00006pt}ell _{1,n}) is bigger than the dimension of the minimal left ideal for (n>4). Hence, we consider the auxiliary real subalgebra of (C hspace{-1.00006pt}ell _{1,n}) to prove a similar statement. We present the multidimensional Dirac–Hestenes equation in (C hspace{-1.00006pt}ell _{1,n}). We prove that one might obtain a solution to the multidimensional Dirac–Hestenes equation using a solution to the multidimensional Dirac equation and vice versa. We also show that the multidimensional Dirac–Hestenes equation has gauge invariance.</div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"35 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Some (mathbb {H})-Banach Modules and Fiber Bundles 一些(mathbb {H}) -Banach模块和光纤束

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-05-08 DOI: 10.1007/s00006-025-01384-9

José Oscar González-Cervantes

引用次数: 0

Slice Regular Holomorphic Cliffordian Functions of Order k k阶的切片正则全纯clifford函数

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-25 DOI: 10.1007/s00006-025-01376-9

Giulio Binosi

引用次数: 0

Additive Preservers of Invertibility or Zero Divisors in Quaternionic Setting 四元数集合中可逆性或零除数的加性保持子

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-22 DOI: 10.1007/s00006-025-01383-w

El Miloud Ouahabi, Khalid Souilah

引用次数: 0

On Monogenic Functions and the Dirac Complex of Two Vector Variables 关于单基因函数和两向量变量的Dirac复形

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-12 DOI: 10.1007/s00006-025-01378-7

Yun Shi, Wei Wang, Qingyan Wu

引用次数: 0

Uncertainty Principles Associated with the Multi-dimensional Quaternionic Offset Linear Canonical Transform 多维四元数偏移线性正则变换的不确定性原理

IF 1.1 2区数学

Advances in Applied Clifford Algebras Pub Date : 2025-04-12 DOI: 10.1007/s00006-025-01379-6

Yingchun Jiang, Sihua Ling, Yan Tang

引用次数: 0