Abstract In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet extended affine group. Firstly, give necessary sufficient conditions existence of nonstationary translates. Using these conditions, prove from We present a representation functions in closure linear span frame sequence terms Fourier transform window functions. show that canonical dual translates has same s...

The efficient solution of operator equations using wavelets requires that they generate a Riesz basis for the underlying Sobolev space, and that they have cancellation properties of a sufficiently high order. Suitable biorthogonal wavelets were constructed on reference domains as the n-cube, which bases have been used, via a domain decomposition approach, as building blocks to construct biortho...

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L(2) (R(2)) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hil...

Fix d≥3 and 10⁡e−tLV|f| are bounded on weighted Lebesgue space Lp(w). The boundedness LV-Riesz potentials LV−α/2 from Lp(w) Lν(wν/p) 0<α≤2, 1<p<dα 1ν=1p−αd will also b...

This paper is devoted to the investigation of Weyl and essential S-spectra a bounded right quaternionic linear operator in Hilbert space. Using Riesz projection, S-eigenvalue finite type both introduced studied. In particular, we have shown that do not contain eigenvalues type. We also described boundary S-spectrum particular case spectral theorem S-spectrum.

Abstract Boundedness of the maximal operator and Calderón–Zygmund singular integral operators in central Morrey–Orlicz spaces were proved papers (Maligranda et al. Colloq Math 138:165–181, 2015; Maligranda Tohoku J 72:235–259, 2020) by second third authors. The weak-type estimates have also been proven. Here we show boundedness Riesz potential corresponding version.

Abstract The aim of this paper is to provide necessary and sufficient conditions on the generator a multiplication operator acting in spaces functions bounded Young Riesz variation so that it is, among other things, invertible, continuous, finite rank, compact, Fredholm or has closed range. Furthermore, we characterize various spectra such operators give some estimates their measure non-compact...

A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis are made by two in a Hilbert space, respectively. In this paper we investigate spectra some multipliers giving, particular, conditions to be at most countable. The contribution extends results available literature about Bessel with symbol decaying zero Riesz bases.