We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The
characterization is obtained as a byproduct of the theoretical foundations of a new method …

In this paper we formulate Donoho and Logan's large sieve principle for the wavelet
transform on the Hardy space, adapting the concept of maximum Nyquist density to the …

We provide a solution to Perelomov's 1972 problem concerning the existence of a phase
transition (known in signal analysis as 'Nyquist rate') determining the basis properties of …

Wavelets are a relatively recent development in applied mathematics. Motivated by the
recent paper [On accumulated spectrograms, Trans. Amer. Math. Soc. 368 (2016) 3629 …

Vector‐valued frames were first introduced under the name of superframes by Balan in the
context of signal multiplexing and by Han and Larson from the mathematical aspect. Since …

Motivated by results of Dyatlov on Fourier uncertainty principles for Cantor sets and by
similar results of Knutsen for joint time-frequency representations (ie, the short-time Fourier …

In this paper, by using the convolution method, we obtain quantitative results in terms of
various moduli of smoothness for approximation of polyanalytic functions by polyanalytic …

In this paper we consider the polyanalytic Fock spaces both in the complex and in the
quaternionic case. In this latter case, the polyanalytic functions are considered in the slice …

We consider a novel bounded integral transform with a kernel function being the n-th
polyanalytic Intissar–Hermite polynomial. We provide a concrete description of its range …

We introduce the concepts of complex polyanalytic weighted Bergman spaces and of
quaternionic polyanalytic weighted Bergman spaces of first and second kind. In these …