Results 31 to 40 of about 257 (144)
Berezin number inequalities for operators
Concrete Operators, 2019 The Berezin transform à of an operator A, acting on the reproducing kernel Hilbert space ℋ = ℋ (Ω) over some (non-empty) set Ω, is defined by Ã(λ) = 〉Aǩ λ, ǩ λ〈 (λ ∈ Ω), where k⌢λ=kλ‖kλ‖${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown ...
Bakherad Mojtaba, Garayev Mubariz T.
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Berezin transform on the quantum unit ball [PDF]
Journal of Mathematical Physics, 2003 We introduce and study, in the framework of a theory of quantum Cartan domains, a q-analog of the Berezin transform on the unit ball. We construct q-analogs of weighted Bergman spaces, Toeplitz operators, and covariant symbol calculus. In studying the analytical properties of the Berezin transform we introduce also the q-analog of the SU(n,1)-invariant
Shklyarov, Dmitry, Zhang, Genkai
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On the $p$-norm of the Berezin transform
Illinois Journal of Mathematics, 2012 Let \(\nu_n\) denote the normalized Lebesgue measure on the unit ball \(B_n\) of \(\mathbb{C}^n\), \(n\geq 1\). Given \(f\in L^1(B_n, \nu_n)\), the Berezin transform \(\mathcal{B}f\) is defined by the formula \[ \mathcal{B} f(z)= (1-|z|^2)^{n+1} \int_{B_n} \frac{f(w)\, d\nu_n(w)}{|1-\langle z, w \rangle|^{2(n+1)}}, \quad z\in B_n.
Liu, Congwen, Zhou, Lifang
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Toeplitz operators with BMO symbols and the Berezin transform
International Journal of Mathematics and Mathematical Sciences, 2003 We prove that the boundedness and compactness of the Toeplitz operator on the Bergman space with a BMO1 symbol is completely determined by the boundary behaviour of its Berezin transform. This result extends the known results in the cases when the symbol
Nina Zorboska
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Covariant derivatives of the Berezin transform [PDF]
Transactions of the American Mathematical Society, 2011 Improving upon recent results of Coburn, Xia, Li, Engliš and Zhang, Bommier-Hato, and others, we give estimates for higher-order covariant derivatives of the Berezin transform of bounded linear operators on a reproducing kernel Hilbert space of holomorphic functions. The answer turns out to involve the curvature of the Bergman-type metric associated to
Engliš, M. (Miroslav), Otáhalová, R.
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Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols
International Journal of Mathematics and Mathematical Sciences, 2011 We study the problem of the boundedness and compactness of 𝑇𝜙 when 𝜙∈𝐿2(Ω) and Ω 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.
Roberto C. Raimondo
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On the commutativity of the Berezin transform
Archiv der MathematikWe consider the commutativity problem for the Berezin transform on weighted Fock spaces. Given a real number $m>0$, for every $α>0$ we denote by $B_α$ the Berezin transform associated to the measure $μ_{m}^α$ with density proportional to $e^{-α|z|^m}$ with respect to Lebesgue measure on the complex plane and normalized so that $μ_ϕ^α(\mathbb C)=1$
Alexander Borichev +2 more
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Time–Frequency Localization Operators and a Berezin Transform [PDF]
Integral Equations and Operator Theory, 2015 Time-frequency localization operators are a quantization procedure that maps symbols on $R^{2d}$ to operators and depends on two window functions. We study the range of this quantization and its dependence on the window functions. If the short-time Fourier transform of the windows does not have any zero, then the range is dense in the Schatten $p ...
Gröchenig, Karlheinz, Bayer, Dominik
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(m,λ)-Berezin Transform on the Weighted Bergman Spaces over the Polydisk
Journal of Function Spaces, 2016 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.
Ran Li, Yufeng Lu
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Schatten Class Toeplitz Operators on the Bergman Space
International Journal of Mathematics and Mathematical Sciences, 2009 We have shown that if the Toeplitz operator Tϕ on the Bergman space La2(𝔻) belongs to the Schatten class Sp,1 ...
Namita Das
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