Banach Journal of Mathematical Analysis最新文献_第8页

Linear preservers of m-selfadjoint operators and high-order isometries m自伴随算子和高阶等距的线性守恒

2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-10-01 DOI: 10.1007/s43037-023-00302-0

Hakima Mohsine, Zouheir Amara, Mourad Oudghiri

引用次数: 0

Harmonic and polyanalytic functional calculi on the S-spectrum for unbounded operators 无界算子s谱上的调和和多解析泛函演算

2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-10-01 DOI: 10.1007/s43037-023-00304-y

Fabrizio Colombo, Antonino De Martino, Stefano Pinton

{"title":"Harmonic and polyanalytic functional calculi on the S-spectrum for unbounded operators","authors":"Fabrizio Colombo, Antonino De Martino, Stefano Pinton","doi":"10.1007/s43037-023-00304-y","DOIUrl":"https://doi.org/10.1007/s43037-023-00304-y","url":null,"abstract":"Abstract Harmonic and polyanalytic functional calculi have been recently defined for bounded commuting operators. Their definitions are based on the Cauchy formula of slice hyperholomorphic functions and on the factorization of the Laplace operator in terms of the Cauchy–Fueter operator $${mathcal{D}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>D</mml:mi> </mml:math> and of its conjugate $$overline{{mathcal{D}}}.$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mover> <mml:mi>D</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> Thanks to the Fueter extension theorem, when we apply the operator $${mathcal{D}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>D</mml:mi> </mml:math> to slice hyperholomorphic functions, we obtain harmonic functions and via the Cauchy formula of slice hyperholomorphic functions, we establish an integral representation for harmonic functions. This integral formula is used to define the harmonic functional calculus on the S -spectrum. Another possibility is to apply the conjugate of the Cauchy–Fueter operator to slice hyperholomorphic functions. In this case, with a similar procedure we obtain the class of polyanalytic functions, their integral representation, and the associated polyanalytic functional calculus. The aim of this paper is to extend the harmonic and the polyanalytic functional calculi to the case of unbounded operators and to prove some of the most important properties. These two functional calculi belong to so called fine structures on the S -spectrum in the quaternionic setting. Fine structures on the S -spectrum associated with Clifford algebras constitute a new research area that deeply connects different research fields such as operator theory, harmonic analysis, and hypercomplex analysis.","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135761239","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: 2

Classification of doubly $${{mathcal {U}}}$$-commuting row isometries 双重$${{mathcal {U}}}$$ -可交换行等距的分类

2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-10-01 DOI: 10.1007/s43037-023-00305-x

Gelu Popescu

引用次数: 0

Characterizations on upper semi-Fredholmness of two-by-two operator matrices 二乘二算子矩阵上半弗雷德霍姆性的表征

2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-10-01 DOI: 10.1007/s43037-023-00306-w

Lili Yang, Xiaohong Cao

引用次数: 0

Characterizations of matrix-valued asymmetric truncated Hankel operators 矩阵值非对称截断Hankel算子的刻画

2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-09-26 DOI: 10.1007/s43037-023-00303-z

Rewayat Khan, Ji Eun Lee

引用次数: 0

Asymptotical behavior of non-autonomous stochastic reaction–diffusion equations with variable delay on $${mathbb {R}}^N$$ 变时滞非自治随机反应扩散方程的渐近性质 $${mathbb {R}}^N$$

2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-09-25 DOI: 10.1007/s43037-023-00301-1

Wenqiang Zhao, Zhi Li

引用次数: 0

Publisher Correction: Quaternionic Gabor frame characterization and the density theorem 出版者更正:四元数Gabor帧表征和密度定理

2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-09-15 DOI: 10.1007/s43037-023-00298-7

Xiao-Li Zhang, Yun-Zhang Li

引用次数: 0

Some new restricted maximal operators of Fejér means of Walsh–Fourier series 沃尔什-傅里叶级数fejsamr均值的一些新的限制极大算子

2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-09-12 DOI: 10.1007/s43037-023-00300-2

Davit Baramidze, Lasha Baramidze, Lars-Erik Perssson, George Tephnadze

{"title":"Some new restricted maximal operators of Fejér means of Walsh–Fourier series","authors":"Davit Baramidze, Lasha Baramidze, Lars-Erik Perssson, George Tephnadze","doi":"10.1007/s43037-023-00300-2","DOIUrl":"https://doi.org/10.1007/s43037-023-00300-2","url":null,"abstract":"Abstract In this paper, we derive the maximal subspace of natural numbers $$left{ n_{k}:kge 0right} ,$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mfenced> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo>:</mml:mo> <mml:mi>k</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mfenced> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> such that the restricted maximal operator, defined by $${sup }_{kin {mathbb {N}}}left| sigma _{n_{k}}Fright| $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mo>sup</mml:mo> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:msub> <mml:mfenced> <mml:msub> <mml:mi>σ</mml:mi> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:msub> <mml:mi>F</mml:mi> </mml:mfenced> </mml:mrow> </mml:math> on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space $$H_{1/2}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>H</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> to the Lebesgue space $$L_{1/2}.$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> The sharpness of this result is also proved.","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135825983","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

Bounded below composition operators on the space of Bloch functions on the unit ball of a Hilbert space 希尔伯特空间的单位球上Bloch函数空间上的复合算子的下界

IF 1.2 2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-09-04 DOI: 10.1007/s43037-023-00295-w

Alejandro Miralles

引用次数: 0

Reflexivity of finite-dimensional sets of operators 有限维算子集的自反性

IF 1.2 2区数学

Banach Journal of Mathematical Analysis Pub Date : 2023-09-01 DOI: 10.1007/s43037-023-00299-6

J. Bračič

引用次数: 0