A \(q\)-analogue of the weighted Bergman space on the disk and associated second \(q\)-Bargmann transform

DOI10.1016/j.jmaa.2016.06.013zbMath1355.30047OpenAlexW2417300428MaRDI QIDQ302089

Abderrahman Essadiq, Allal Ghanmi, Ahmed Intissar

Publication date: 4 July 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.06.013

zbMATH Keywords

\(q\)-hypergeometric functions\(q\)-Laguerre polynomialssecond \(q\)-Bargmann transformweighted \(q\)-Bergman space

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Bergman spaces and Fock spaces (30H20)

Related Items

Uncertainty principles of Heisenberg type for the Bargmann transform, A Banach algebra structure on the $q$-Bergman space and related topics, Toeplitz operators and composition operators on the \(q\)-Bergman space, The slice hyperholomorphic Bergman space on \(\mathbb {B}_{R}\): integral representation and asymptotic behavior

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lectures on Gaussian integral operators and classical groups
• Jacobi functions as limit cases of q-ultraspherical polynomials
• Limits of some q-Laguerre polynomials
• The q-analogue of the Laguerre polynomials
• The \(q\)-Laguerre polynomials and related moment problems
• The moment problem associated with the \(q\)-Laguerre polynomials
• Generalized second Bargmann transforms associated with the hyperbolic Landau levels on the Poincaré disk
• Analysis on Fock Spaces
• On a Hilbert space of analytic functions and an associated integral transform part I
• A Generalization of Moak's q-Laguerre Polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Chapter 16 of Ramanujan’s second notebook: theta-functions and 𝑞-series
• Ramanujan's Extensions of the Gamma and Beta Functions
• Harmonic Analysis in Phase Space. (AM-122)
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen