On bicomplex Fourier--Wigner transforms

2019/04/20 by Gourari, Aiad El, Ghanmi, Allal, Zine, Khalil
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1904.09440

Abstract

We consider the 1- and 2-d bicomplex analogs of the classical Fourier--Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex--polyanalytic functional spaces are discussed. Particular case of special window is also considered. An orthogonal basis for the space of bicomplex--valued square integrable functions on the bicomplex numbers is constructed by means of the polyanalytic complex Hermite functions.

Related

• Bicomplex analogs of Segal-Bargmann and fractional Fourier transforms
• Bivariate poly-analytic Hermite polynomials
• Inverse Fourier Transform for Bi-Complex Variables
• The Bicomplex-Real Calculus and Applications to Bicomplex Hermite-Itô Polynomials
• Complex Hermite functions as Fourier-Wigner transform