Toeplitz operators with vertical symbols acting on the poly-Bergman spaces of the upper half-plane

DOI10.1007/s11785-015-0469-4zbMath1343.47081OpenAlexW244932629MaRDI QIDQ889968

Armando Sánchez-Nungaray, Josué Ramírez-Ortega

Publication date: 9 November 2015

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-015-0469-4

zbMATH Keywords

poly-Bergman spacealgebras of Toeplitz operatorspoly-Bergman projectionspecial symbols

Mathematics Subject Classification ID

Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) (47L80) Spaces and algebras of analytic functions of one complex variable (30H99)

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Toeplitz operators with homogeneous symbols acting on the poly-Bergman spaces of the upper half-plane ⋮ Translation-invariant operators in reproducing kernel Hilbert spaces ⋮ Construction of some classes of commutative Banach and \(C^{\star}\)-algebras of Toeplitz operators ⋮ Weighted Bergman spaces associated with the hyperbolic group ⋮ Radial Operators on Polyanalytic Bargmann–Segal–Fock Spaces ⋮ Algebra Generated by a Finite Number of Toeplitz Operators with Homogeneous Symbols Acting on the Poly-Bergman Spaces ⋮ Toeplitz operators acting on true-poly-Bergman type spaces of the two-dimensional Siegel domain: nilpotent symbols ⋮ Homogeneously polyanalytic kernels on the unit ball and the Siegel domain ⋮ Toeplitz operators with homogeneous symbols on polyharmonic spaces ⋮ Toeplitz operators with horizontal symbols acting on the poly-Fock spaces ⋮ Toeplitz localization operators: spectral functions density ⋮ Radial operators on polyanalytic weighted Bergman spaces ⋮ Toeplitz operators with vertical symbols acting on the Poly-Bergman spaces of the upper half-plane. II

Cites Work

• On the structure of Bergman and poly-Bergman spaces
• On \(C^\ast\)-algebras of Toeplitz operators on the harmonic Bergman space
• Commutative algebras of Toeplitz operators on the Bergman space
• Commutative \(C^{\ast}\)-algebras of Toeplitz operators and quantization on the unit disk
• On Toeplitz operators on the weighted harmonic Bergman space on the upper half-plane
• Toeplitz Operators on the Bergman Spaces with Pseudodifferential Defining Symbols
• The Structure of Certain Operator Algebras
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