Published in Forum Mathematicum
We deduce continuity, compactness and invariance properties for quasi-Banach Orlicz modulation spaces on ℝ d {\mathbb{R}^{d}} . We characterize such spaces in terms of Gabor expansions and by their images under the Bargmann transform.
Published in Analysis
In this paper, we extend the continuous wavelet transform to Schwartz distributions in D ′ ( R n ) \mathcal{D}^{\prime}(\mathbb{R}^{n}) , n ≥ 1 n\geq 1 , and derive the corresponding wavelet inversion formula (valid modulo a constant distribution) interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is an...
Published in Nonlinearity
We extend the classical Euler–Maclaurin (EM) expansion to sums over multidimensional lattices that involve functions with algebraic singularities. This offers a tool for a precise and fast evaluation of singular sums that appear in multidimensional long-range interacting systems. We find that the approximation error decays exponentially with the ex...
Published in Proceedings - Mathematical Sciences
In this paper, we study the Mexican hat wavelet transform (MHWT) of generalized function space G′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G}'$$\end{doc...
Published in Mediterranean Journal of Mathematics
We consider the existence of convolution of Roumieu type ultradistribution with the kernel es(1+|x|2)q/2,q≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e^{s(1+|x|^2...
Published in Journal of Nonlinear Science
In the setting of a product of distributions, we define a concept of a solution for the Brio system ut+12(u2+v2)x=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_{t}...
Published in Advances in Operator Theory
We consider several general sequential conditions for convolvability of two Roumieu ultradistributions on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}...
Published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
The powers δr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta ^r$$\end{document} and (δ′)r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} ...
Published in Zeitschrift für angewandte Mathematik und Physik
This paper studies a Riemann problem for the isentropic Euler equations and addresses two gaps in the literature concerning positive pressures. Such study is made using a product of distributions and a solution concept that extends the classical solution concept. Under certain conditions, even for positive pressures, it is shown that the Riemann pr...
Published in Computational and Applied Mathematics
An identity showing that any positive real power of the Heaviside function is almost everywhere equal to the Heaviside function of power 1 is proved in this paper. A similar identity is shown to hold for corresponding distributions. The identity is then used to attach a specific meaning to the nonlinear Green’s function of quasi-linear ordinary dif...
