scholarly journals Spectral aspects of the Berezin transform

2020 ◽  
Vol 3 ◽  
pp. 1343-1387
Author(s):  
Louis Ioos ◽  
Victoria Kaminker ◽  
Leonid Polterovich ◽  
Dor Shmoish
Keyword(s):  
Berezin Transform

scholarly journals The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

2021 ◽  
Author(s):  
Cezhong Tong ◽  
Junfeng Li ◽  
Hicham Arroussi
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Kernel Estimates ◽  
Berezin Transforms

AbstractIn this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.

scholarly journals Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Roberto C. Raimondo
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Boundary Behavior ◽  
Berezin Transform ◽  
Planar Domain ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Planar Domains ◽  
Necessary And Sufficient ◽  
The Relationship

We study the problem of the boundedness and compactness of when and is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of

scholarly journals Properties of the Berezin transform of bounded functions

1999 ◽  
Vol 59 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Jaesung Lee
Keyword(s):  
Unit Circle ◽  
Convex Combination ◽  
Berezin Transform ◽  
Direct Sum ◽  
Bounded Functions

We find the spectrum of the Berezin operator T on L∞(Bn), then we show that if f ∈ L∞(Bn) satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of T, then f is M-harmonic.Finally we decompose the subspace of L∞(Bn) where lim Tkf exists into the direct sum of two subspaces of L∞(Bn).

scholarly journals Berezin transform in polynomial bergman spaces

2010 ◽  
Vol 63 (12) ◽  
pp. 1533-1584 ◽  
Author(s):  
Yacin Ameur ◽  
Nikolai Makarov ◽  
Håkan Hedenmalm
Keyword(s):  
Bergman Spaces ◽  
Berezin Transform

scholarly journals Weighted estimates for the Berezin transform and Bergman projection on the unit ball

2016 ◽  
Vol 286 (3-4) ◽  
pp. 1465-1478 ◽  
Author(s):  
Rob Rahm ◽  
Edgar Tchoundja ◽  
Brett D. Wick
Keyword(s):  
Unit Ball ◽  
Berezin Transform ◽  
Bergman Projection ◽  
Weighted Estimates

scholarly journals (m,λ)-Berezin Transform on the Weighted Bergman Spaces over the Polydisk

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Ran Li ◽  
Yufeng Lu
Keyword(s):  
Linear Operator ◽  
Bergman Space ◽  
Bounded Linear Operator ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Main Tool ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Bounded Linear

We prove that every bounded linear operator on weighted Bergman space over the polydisk can be approximated by Toeplitz operators under some conditions. The main tool here is the so-called(m,λ)-Berezin transform. In particular, our results generalized the results of K. Nam and D. C. Zheng to the case of operators acting onAλ2(Dn).

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