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Weighted Bergman Kernels and Mathematical Physics
Axioms, 2020 We review several results in the theory of weighted Bergman kernels. Weighted Bergman kernels generalize ordinary Bergman kernels of domains Ω ⊂ C n but also appear locally in the attempt to quantize classical states of mechanical systems ...
Elisabetta Barletta +2 more
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Abstract and Applied Analysis, 2011 Let ψ be a holomorphic mapping on the upper half-plane Π+={z∈ℂ:Jz>0} and φ be a holomorphic self-map of Π+. We characterize bounded weighted composition operators acting from the weighted Bergman space to the weighted-type space on the upper half-plane ...
Stevo Stević +2 more
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Weighted Composition Operators from Generalized Weighted Bergman Spaces to Weighted-Type Spaces
Journal of Inequalities and Applications, 2009 Let φ be a holomorphic self-map and let ψ be a holomorphic function on the unit ball B. The boundedness and compactness of the weighted composition operator ψCφ from the generalized weighted Bergman space into a class of ...
Dinggui Gu
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The Zero Product of Toeplitz Operators on the 2-Analytic Weighted Bergman Space
Journal of Function SpacesTwo-analytic weighted Bergman space is a nonanalytic function space which is closely related to analytic functions. In this paper, we mainly discuss the zero product problem for Toeplitz operators on the 2-analytic weighted Bergman space.
Xia Wang +3 more
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The backward shift on weighted Bergman spaces.
Michigan Mathematical Journal, 1996 The authors study the backward shift-invariant subspaces of the weighted Bergman spaces \(A_\alpha^p\) for \(\alpha>-1\) and \(1\leq ...
Aleman, Alexandru, Ross, William T.
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Equivalent Bergman Spaces with Inequivalent Weights [PDF]
The Journal of Geometric Analysis, 2018 We give a proof that every space of weighted square-integrable holomorphic functions admits an equivalent weight whose Bergman kernel has zeroes. Here the weights are equivalent in the sense that they determine the same space of holomorphic functions.
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Finite-rank intermediate Hankel operators on the Bergman space
International Journal of Mathematics and Mathematical Sciences, 2001 Let L2=L2(D,r dr dθ/π) be the Lebesgue space on the open unit disc and let La2=L2∩ℋol(D) be the Bergman space. Let P be the orthogonal projection of L2 onto La2 and let Q be the orthogonal projection onto L¯a,02={g∈L2;g¯∈La2, g(0)=0}. Then I−P≥Q.
Takahiko Nakazi, Tomoko Osawa
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Compact differences of weighted composition operators on the weighted Bergman spaces
Journal of Inequalities and Applications, 2017 In this paper, we consider the compact differences of weighted composition operators on the standard weighted Bergman spaces. Some necessary and sufficient conditions for the differences of weighted composition operators to be compact are given, which ...
Maocai Wang, Xingxing Yao, Fen Chen
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Toeplitz Operators on Fock Space over
Axioms, 2023 The first goal of this paper is to find a representation of the Fock space on Cn in terms of the weighted Bergman spaces of the projective spaces CPn−1; i.e., every function in the Fock space can be written as a direct sum of elements in weighted Bergman
Carlos González-Flores +3 more
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Canonical isometry on weighted Bergman spaces [PDF]
Pacific Journal of Mathematics, 1989 Let u be an absolutely continuous measure on a domain \(D\subset \mathbb{C}^ N\) with a strictly positive continuous Radon-Nikodym derivative with respect to the Lebesgue measure. Let \(G(u)\) be the group of biholomorphic automorphisms \(\varphi\) of \(D\) which leave u invariant modulo holomorphic change of gauge (i.e.
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