scholarly journals A reproducing kernel thesis for operators on Bergman-type function spaces

2014 ◽  
Vol 267 (7) ◽  
pp. 2028-2055 ◽  
Author(s):  
Mishko Mitkovski ◽  
Brett D. Wick
Keyword(s):  
Reproducing Kernel ◽  
Function Spaces ◽  
Type Function ◽  
Reproducing Kernel Thesis

scholarly journals Functional Representations for Fock Superalgebras

1998 ◽  
Vol 01 (02) ◽  
pp. 285-324 ◽  
Author(s):  
Joachim Kupsch ◽  
Oleg G. Smolyanov
Keyword(s):  
Reproducing Kernel ◽  
Fock Space ◽  
Function Spaces ◽  
Graded Algebras ◽  
Fock Representation ◽  
Infinite Dimensional ◽  
Gaussian Integration ◽  
Classical Function ◽  
Functional Representations ◽  
Wick Ordering

The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite-dimensional superspaces, and construct super-analogs of the classical function spaces with a reproducing kernel — including the Bargmann–Fock representation — and of the Wiener–Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein–Uhlenbeck semigroup on the Fock space.

scholarly journals Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators

2010 ◽  
Vol 259 (10) ◽  
pp. 2673-2701 ◽  
Author(s):  
Anton Baranov ◽  
Isabelle Chalendar ◽  
Emmanuel Fricain ◽  
Javad Mashreghi ◽  
Dan Timotin
Keyword(s):  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Reproducing Kernel Thesis

scholarly journals Some results concerning localization property of generalized Herz, Herz-type Besov spaces and Herz-type Triebel-Lizorkin spaces

2021 ◽  
Vol 13 (1) ◽  
pp. 217-228
Author(s):  
A. Djeriou ◽  
R. Heraiz
Keyword(s):  
Besov Spaces ◽  
Function Spaces ◽  
Homogeneous Case ◽  
Negative Numbers ◽  
Type Function ◽  
Localization Property

In this paper, based on generalized Herz-type function spaces $\dot{K}_{q}^{p}(\theta)$ were introduced by Y. Komori and K. Matsuoka in 2009, we define Herz-type Besov spaces $\dot{K}_{q}^{p}B_{\beta }^{s}(\theta)$ and Herz-type Triebel-Lizorkin spaces $\dot{K}_{q}^{p}F_{\beta }^{s}(\theta)$, which cover the Besov spaces and the Triebel-Lizorkin spaces in the homogeneous case, where $\theta=\left\{\theta(k)\right\} _{k\in\mathbb{Z}}$ is a sequence of non-negative numbers $\theta(k)$ such that \begin{equation*} C^{-1}2^{\delta (k-j)}\leq \frac{\theta(k)}{\theta(j)} \leq C2^{\alpha (k-j)},\quad k>j, \end{equation*} for some $C\geq 1$ ($\alpha$ and $\delta $ are numbers in $\mathbb{R}$). Further, under the condition mentioned above on ${\theta }$, we prove that $\dot{K}_{q}^{p}\left({\theta }\right)$ and $\dot{K}_{q}^{p}B_{\beta }^{s}\left({\theta }\right)$ are localizable in the $\ell _{q}$-norm for $p=q$, and $\dot{K}_{q}^{p}F_{\beta }^{s}\left({\theta }\right)$ is localizable in the $\ell _{q}$-norm, i.e. there exists $\varphi \in \mathcal{D}({\mathbb{R}}^{n})$ satisfying $\sum_{k\in \mathbb{Z}^{n}}\varphi \left( x-k\right) =1$, for any $x\in \mathbb{R}^{n}$, such that \begin{equation*} \left\Vert f|E\right\Vert \approx \Big(\underset{k\in \mathbb{Z}^{n}}{\sum }\left\Vert \varphi (\cdot-k)\cdot f|E\right\Vert ^{q}\Big)^{1/q}. \end{equation*} Results presented in this paper improve and generalize some known corresponding results in some function spaces.

scholarly journals Uniform limit power-type function spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Chuanyi Zhang ◽  
Weiguo Liu
Keyword(s):  
Power Function ◽  
Function Spaces ◽  
Power Functions ◽  
Power Type ◽  
Uniform Limit ◽  
Type Function ◽  
Limit Power

To answer a question proposed by Mari in 1996, we propose𝒰ℒ𝒫α(ℝ+), the space of uniform limit power functions. We show that𝒰ℒ𝒫α(ℝ+)has properties similar to that of𝒜𝒫(ℝ+). We also proposed three other limit power function spaces.

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