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arXiv · 1904.09440

On bicomplex Fourier--Wigner transforms

Aiad El Gourari·Allal Ghanmi·Khalil Zine
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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.

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Aiad El Gourari, Allal Ghanmi, Khalil Zine. 2019-04-20. On bicomplex Fourier--Wigner transforms. https://arxiv.org/abs/1904.09440

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