Generalized Fock Spaces and Associated Operators

DOI10.1137/0515015zbMath0596.46017OpenAlexW2072035632MaRDI QIDQ3728629

F. M. Cholewinski

Publication date: 1984

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0515015

zbMATH Keywords

reproducing kernelWeyl relationsBessel function of the third kindgeneralized Fock spaces associated with Bessel functionsHilbert space of even entire functions weighted by a modifiedHilbert space of even entire functions weighted by a modified Bessel function of the third kindSchrödinger radial kinetic energy operator

Mathematics Subject Classification ID

Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items (23)

Segal-Bargmann transforms associated with finite Coxeter groups ⋮ Fock-type spaces associated to higher-order Bessel operator ⋮ THE μ-DEFORMED SEGAL–BARGMANN TRANSFORM IS A HALL TYPE TRANSFORM ⋮ Generalized Fock spaces and the Stirling numbers ⋮ On the images of Dunkl-Sobolev spaces under the Schrödinger semigroup associated to Dunkl operators ⋮ Hankel-type Segal-Bargmann transform and its applications to UP and PDEs ⋮ Heisenberg uncertainty principles for the Dunkl-type Fock space ⋮ Reproducing kernel Hilbert spaces (RKHS) for the higher order Bessel operator ⋮ Fock spaces for the complex Dunkl operator and deformed \(\mathrm{su}(1,1)\) algebra ⋮ Inversion formula and uncertainty inequalities for the Weinstein-type Segal–Bargmann transform ⋮ Uncertainty principles for the Weinstein type Segal-Bargmann space ⋮ Difference and primitive operators on the Dunkl-type Fock SPACE \(\mathscr{F}_{\alpha }(\mathbb{C}^d)\) ⋮ DIRECT AND REVERSE LOG-SOBOLEV INEQUALITIES IN μ-DEFORMED SEGAL–BARGMANN ANALYSIS ⋮ Some examples of extremal functions on the Dunkl-type Fock space \(F_k(\mathbb C)\) ⋮ Analytical and numerical approximation formulas on the Dunkl-type Fock spaces ⋮ Analyticity of the Schrödinger propagator on the Heisenberg group ⋮ Generalized Fock spaces and Weyl relations for the Dunkl kernel on the real line ⋮ Infinite dimensional fock spaces and schrödinger equation solutions ⋮ Infinite dimensional Fock spaces and associated creation and annihilation operators ⋮ Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels ⋮ Inversion formulas for the Dunkl-type Segal–Bargmann transform ⋮ APPLICATIONS ON THE BESSEL-STRUVE-TYPE FOCK SPACE ⋮ Coherent states of the one-dimensional Dunkl oscillator for real and complex variables and the Segal–Bargmann transformation of Dunkl-type

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