Horizontal Fourier transform of the polyanalytic Fock kernel

DOI10.1007/s00020-024-02772-9MaRDI QIDQ6596301

Erick Lee-Guzmán, Armando Sánchez-Nungaray, Egor A. Maksimenko, Gerardo Ramos-Vazquez

Publication date: 2 September 2024

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

Fourier transformunitary representationLaguerre polynomialreproducing kernelHermite polynomialpolyanalytic functiontranslation-invariant operatorsBargmann-Segal-Fock space

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) (30G20) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32) Bergman spaces and Fock spaces (30H20)

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