Inversion formulas for the Dunkl-type Segal–Bargmann transform

DOI10.1080/10652469.2015.1004331zbMath1312.30045OpenAlexW1966046781MaRDI QIDQ5246271

Fethi Soltani

Publication date: 20 April 2015

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2015.1004331

zbMATH Keywords

Toeplitz operatorsFock spacesSegal-Bargmann transformspaces of entire functions

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Special classes of entire functions of one complex variable and growth estimates (30D15) Spaces and algebras of analytic functions of one complex variable (30H99) Bergman spaces and Fock spaces (30H20)

Related Items (3)

Hankel-type Segal-Bargmann transform and its applications to UP and PDEs ⋮ Inversion formula and uncertainty inequalities for the Weinstein-type Segal–Bargmann transform ⋮ Uncertainty principles for the Dunkl-type Segal-Bargmann transform

Cites Work

• Best approximation formulas for the Dunkl \(L^2\)-multiplier operators on \(\mathbb{R}^{d}\)
• Generalized Fock spaces and Weyl relations for the Dunkl kernel on the real line
• The Dunkl transform
• \(L^{p}\)-Fourier multipliers for the Dunkl operator on the real line.
• Generalized Fock spaces and Weyl commutation relations for the Dunkl kernel.
• Exact operator solution of the Calogero-Sutherland model
• Multiplier operators and extremal functions related to the dual Dunkl-Sonine operator
• Some results on Tchebycheffian spline functions and stochastic processes
• Best approximation, Tikhonov regularization and reproducing kernels
• Toeplitz and Translation Operators on the q-Fock Spaces
• Multiplication and Translation Operators on the Fock Spaces for the q-Modified Bessel Function
• The weierstrass transform and an isometry in the heat equation
• On a Hilbert space of analytic functions and an associated integral transform part I
• Generalized Fock Spaces and Associated Operators
• Integral Kernels with Reflection Group Invariance
• Approximate real inversion formulas of the gaussian convolution
• Approximate and analytical inversion formulas in heat conduction on multidimensional spaces
• Inversion formulas in the Dunkl-type heat conduction on

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