On bicomplex Fourier--Wigner transforms
Complex Variables
2019-04-23 v1 Functional Analysis
Abstract
We consider the - and -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.
Cite
@article{arxiv.1904.09440,
title = {On bicomplex Fourier--Wigner transforms},
author = {Aiad El Gourari and Allal Ghanmi and Khalil Zine},
journal= {arXiv preprint arXiv:1904.09440},
year = {2019}
}
Comments
12 pages