Results 111 to 120 of about 257 (144)
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The Berezin Transform and Its Applications
Acta Mathematica Scientia, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kehe Zhu
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m-Berezin Transform on the Polydisk
Integral Equations and Operator Theory, 2005m-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.
Dechao Zheng
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Graduate Texts in Mathematics, 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
Kehe Zhu
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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
Kehe Zhu
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Invariant Operators and the Berezin Transform on Cartan Domains
Mathematische Nachrichten, 1998AbstractLet Ω be an irreducible Cartan domain of rank r and genus p and Bv (c > p ‐ 1) be the Berezin transform on Ω. It is known that as v tends to infinity, the Berezin transform admits the asymptotic expansion Bν∼∑k=0∞ Qkν−k where the Qk's are certain invariant differential operators — for instance, Q0 is the identity and Q1 is the Laplace ...
Miroslav Englis
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Domination of Berezin Transform
Vietnam Journal of Mathematics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Das, Namita, Sahoo, Madhusmita
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Berezin Transform for Solvable Groups
Acta Applicandae Mathematica, 2004The authors study the Berezin transform for the multi-weighted Bergman spaces \(H^2_\nu(D)=\{h\in L^2(D,d\mu_\nu): h\) holomorphic\} of Gindikin type on homogeneous cones and Siegel domains \(D,\) depending on a vector parameter \(\nu=(\nu_1,\ldots,\nu_r).\) Using an explicit kernel representation for the associated eigen-operators they provide its ...
Arazy, Jonathan, Upmeier, Harald
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The Range of the Berezin Transform
Journal of Mathematical Sciences, 2017Let \(H(\mathbb{D})\) 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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Berezin Transform, Mellin Transform and Toeplitz Operators
Complex Analysis and Operator Theory, 2010Let \(B\) be the Berezin transform associated with the Bergman space. The authors of the article under review improve a theorem of \textit{P. Ahern} [J. Funct. Anal. 215, No. 1, 206--216 (2004; Zbl 1088.47014)]. Namely, they show that, if \(u\in L^1\) and \(Bu\) is a harmonic function, then \(u\) itself is harmonic.
Čučković, Željko, Li, Bo
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Complex Analysis and Operator Theory, 2007
We give examples of pseudoconvex Reinhardt domains where the Berezin transform has integral kernel with singularities and, hence, fails to be a smoothing map. On the other hand, we show that this can never happen for a plane domain – in fact, then the Bergman kernel is always either identically zero or strictly positive everywhere on the diagonal – and
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We give examples of pseudoconvex Reinhardt domains where the Berezin transform has integral kernel with singularities and, hence, fails to be a smoothing map. On the other hand, we show that this can never happen for a plane domain – in fact, then the Bergman kernel is always either identically zero or strictly positive everywhere on the diagonal – and
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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 +2 more
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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 +2 more
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