On the polyanalytic short-time Fourier transform in the quaternionic setting

DOI10.3934/cpaa.2022117OpenAlexW3205635031MaRDI QIDQ2691516

Antonino De Martino, Kamal Diki

Publication date: 29 March 2023

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.04520

zbMATH Keywords

quaternionsshort-time Fourier transformslice hyperholomorphic functionsBargmann transformslice polyanalytic functions

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) General harmonic expansions, frames (42C15) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Related Items (11)

A polyanalytic functional calculus of order 2 on the 𝑆-spectrum ⋮ Generalized Appell polynomials and Fueter–Bargmann transforms in the polyanalytic setting ⋮ Harmonic and polyanalytic functional calculi on the \(S\)-spectrum for unbounded operators ⋮ Superoscillations and Fock spaces ⋮ On the Mittag Leffler Bargmann (MLB) transform ⋮ The \(\mathcal{F}\)-resolvent equation and Riesz projectors for the \(\mathcal{F}\)-functional calculus ⋮ Properties of a polyanalytic functional calculus on the S‐spectrum ⋮ Spectral properties of weighted Cauchy singular integral transform on S-poly-Bargmann spaces ⋮ Short time quadratic-phase quaternionic Fourier transform and associated uncertainty principle ⋮ Density of complex and quaternionic polyanalytic polynomials in polyanalytic Fock spaces ⋮ On a new characterization of the true-poly-analytic Bargmann spaces

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