ABSTRACT
In 1990, van Eijndhoven and Meyers provide a special orthonormal basis for the Bargmann Hilbert space consisting of holomorphic Hermite functions. Then it was be natural to look for its orthogonal complement in the underlying -Hilbert space. In this paper, we describe the orthogonal complement of this Hilbert space. More precisely, a polyanalytic orthonormal basis is given and the explicit expressions of the corresponding reproducing kernel functions and Segal–Bargmann integral transforms are provided. The obtained basis are then used to provide a non-trivial - and -fractional like-Fourier transforms.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Allal Ghanmi http://orcid.org/0000-0003-0764-5576