Results 121 to 130 of about 254 (149)

The Berezin Transform

2000
In this chapter we consider an analogue of the Poisson transform in the context of Bergman spaces, called the Berezin transform. We show that its fixed points are precisely the harmonic functions. We introduce a space of BMO type on the disk, the analytic part of which is the Bloch space, and characterize this space in terms of the Berezin transform.
Haakan Hedenmalm, Boris Korenblum, Kehe Zhu   +2 more
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Berezin transform of slice functions

Complex Variables and Elliptic Equations, 2016
In a recent paper, we introduced the Berezin transform of quaternionic linear operators and we obtained some properties in the setting of weighted Bergman spaces of slice hyperholomorphic functions. Here, we define the Berezin transform of slice functions, which corresponds to the case of a multiplication operator by certain quaternion-valued slice ...
Colombo, F., Gantner, J., Janssens, T.
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Berezin Transform in Clifford Analysis

AIP Conference Proceedings, 2008
In the weighted monogenic Bergman spaces A2(Bn,Ll0,n,dVα), the Berezin transform of a bounded continuous function f tends to itself pointwise as the parameter α tends to infinity. As a consequence, the norm of the Toeplitz operator ‖Tf(α)‖ tends to ‖f‖∞ as α tends to infinity.
Guangbin Ren, Liang Liu
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The Range of the Berezin Transform

Journal of Mathematical Sciences, 2017
Let \(H(\mathbb{D})\) be the space of holomorphic functions on the open unit disk \(\mathbb{D}\subset\mathbb{C}\) and let \(B(u)\) be the Berezin transform of a function \(u\in L^1(\mathbb{D})\). In this paper the authors give a description of the functions \(\varphi=\sum_{j=1}^N f_j\overline{g}_j\), \(f_j, g_j\in H(\mathbb{D})\), in the range of \(B\).
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m-Berezin Transform on the Polydisk

Integral Equations and Operator Theory, 2005
m-Berezin transforms are introduced for bounded operators on the Bergman space of the polydisk. We show several properties of m-Berezin transform and use them to show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary of the polydisk.
Kyesook Nam, Dechao Zheng
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Berezin transform on¶compact Hermitian symmetric spaces

manuscripta mathematica, 1998
\textit{A. Unterberger} and \textit{H. Upmeier} [Math. Commun. Phys. 164, 563-597 (1994; Zbl 0843.32019)] studied the Berezin transform on the irreducible noncompact Hermitian symmetric space \(D = G/K\) and obtained the spectral decomposition of the Berezin transform operator on \(L^2 (D)\) under the irreducible decomposition of \(L^2(D)\) into ...
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The Berezin Transform and BMO

2012
In this chapter, we study the Berezin transform on F α 2 and certain spaces of functions of bounded mean oscillation (BMO) on the complex plane. We first consider the Berezin symbol of a bounded linear operator on F α 2 and show that this is a Lipschitz function in the Euclidean metric. We then consider the Berezin transform of a function and show that
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Inequalities Involving Berezin Norm and Berezin Number

Complex Analysis and Operator Theory, 2022
Kallol Paul
exaly  

On a New Norm on the Space of Reproducing Kernel Hilbert Space Operators and Berezin Radius Inequalities

Numerical Functional Analysis and Optimization, 2023
Kallol Paul
exaly  

Berezin Transform and a Deformation Decomposition

2014
We present a new form for a deformation decomposition of the Berezin transform in polynomial quantization on para-Hermitian symmetric spaces.
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