Results 151 to 160 of about 5,186,045 (202)

Toeplitz Operators on the Dirichlet Space

Integral Equations and Operator Theory, 2010
Let \(D\) be the open unit disk in the complex plane \(\mathbb{C}\) and let \(dA\) denote the Lebesgue measure on \(D\). The Sobolev space \(W^{1,2}(D)\) consists of functions \(u\) with weak derivatives in \(D\), for which the norm is defined by \[ \|u\|:=\left(\left|\int_Du\,dA\right|^2+ \int_D\left(\left|\frac{\partial{u}}{\partial{z}}\right|^2 ...
Tao Yu
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Hypercyclicity of weighted composition operators on a weighted Dirichlet space

Complex Variables and Elliptic Equations, 2014
Li Zhang, Ze‐hua Zhou
semanticscholar   +3 more sources

$$\ell ^p$$-Type Dirichlet Spaces

Mediterranean Journal of Mathematics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
P. J. Gerlach-Mena, J. Müller
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Toeplitz Operators on Dirichlet Spaces

Acta Mathematica Sinica, English Series, 2001
Let \(B_n\) be the unit ball in \(\mathbb{C}^n\) and \(\mathcal{D}\) the Dirichlet space, that is, the subspace of analytic functions in the Sobolev space with the norm \[ \left[\sum_{i=1}^n\int_{B_n}\left(\left|\frac{\partial f}{\partial z_i}(z)^2+ \frac{\partial f}{\partial \overline{z_i}}(z)^2 \right|\right) dv\right]^\frac{1}{2}.
Lu, Yu Feng, Sun, Shun Hua
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Kato Space for Dirichlet Forms

Potential Analysis, 1999
The authors consider a wide class of regular Dirichlet forms of diffusion type incuding elliptic and subelliptic operators. For these Dirichlet forms the notion of Kato space is introduced and it is proved that the Kato space becomes a Banach space when suitably normed.
BIROLI, MARCO, MOSCO U.
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Algebraic Structure on Dirichlet Spaces

Acta Mathematica Sinica, English Series, 2005
The authors give a few equivalent conditions for a closed form \((\mathcal E,\mathcal F)\) on an \(L^2\)-space to be Markovian. It is well known that the semigroup generated by \(\mathcal E\) is sub-Markovian if and only if the unit/normal contractions operate on \(\mathcal E\). One of the equivalent properties reads as follows: the space \({\mathcal F}
Fang, Xing, He, Ping, Ying, Jian Gang
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Hankel Matrices Acting on the Dirichlet Space

Journal of Fourier Analysis and Applications
The study of the infinite Hankel matrix acting on analytic function spaces dates back to the influential work of Nehari and Widom on the Hardy space H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts ...
Guanlong Bao, Kunyu Guo, Fangmei Sun, Zipeng Wang   +3 more
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Multipliers on Dirichlet Type Spaces

Acta Mathematica Sinica, English Series, 2001
The authors consider the weighted Dirichlet space \({\mathcal D}_\tau \) of the unit ball in \({\mathbb C}^n \). These spaces include the classical Dirichlet space (\(\tau=1 \)), the Hardy space (\(\tau=0 \)), and the Bergman space (\(\tau=-1 \)), and are defined in the paper in the standard way via their Taylor coefficients. A complex-valued function \
Hu, Peng Yan, Shi, Ji Huai
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A class of quasicontractive semigroups acting on Hardy and Dirichlet space

, 2015
This paper provides a complete characterization of quasicontractive C0-semigroups on Hardy and Dirichlet space with a prescribed generator of the form $${Af=Gf^\prime}$$Af=Gf′ . We show that such semigroups are semigroups of composition operators, and we
C. Avicou, I. Chalendar, J. Partington
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Reflected Dirichlet Spaces

2011
This chapter turns to reflected Dirichlet spaces. It first introduces the notion of terminal random variables and harmonic functions of finite energy for a Hunt process associated with a transient regular Dirichlet form. The chapter next establishes several equivalent notions of reflected Dirichlet space (ℰ ref,ℱ ref)
Zhen-Qing Chen, Masatoshi Fukushima
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