Abstract For integers n, q= 1, 2, 3,…, let Pol n, q denote the C-linear space of polynomials in
z and ̄z, of degree≤ n− 1 in z and of degree≤ q− 1 in ̄z. We supply Pol n, q with the inner …

We develop the quantum harmonic analysis framework in the reducible setting and apply
our findings to polyanalytic Fock spaces. In particular, we explain some phenomena …

We develop an alternative approach to the study of Fourier series, based on the Short-Time-
Fourier Transform (STFT) acting on $ L_ {\nu}^{2}(0, 1) $, the space of measurable functions …

In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of
infinite order. First we study in details the counterpart of the Fock space and related results in …

To a higher Landau level corresponds a generalized Poisson distribution arising from
generalized coherent states. In this paper, we write down the atomic decomposition of this …

We propose the Lie-algebraic interpretation of poly-analytic functions in L_2 (C, d μ) L 2 (C,
d μ), with the Gaussian measure d μ d μ, based on a flag structure formed by the …

We provide a concrete characterization of the poly-analytic planar automorphic functions, a
special class of non analytic planar automorphic functions with respect to the Appell …

Special generating functions and Mehler's formula for the univariate complex Hermite
polynomials are obtained and next employed to introduce and study some one-and two …

Let D be either D or C, and let J be either [0, 1] or R+, so that D= J× T, where T is the unit
circle in C. We set H for any weighted Hilbert space L 2 (D, d ν), with the probability measure …

For a given discrete subgroup Γ of (C,+) and given real number ν> 0⁠, we study the spectral
properties of the magnetic Laplacian operator Δ ν acting on the Hilbert space L Γ, χ 2, ν (C) …