Approximation from shift-invariant spaces with smooth generators

In this paper, we examine the convergence of sampling expansions in shift-invariant spaces with smooth generators for fundamentally large classes of functions. We establish the rate of approximation of a signal (not necessarily continuous) by the sampling series in terms of an Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>p$$\end{document}-average modulus of smoothness. We investigate the convergence and error analysis of sampling and projection operators based on Gaussian generators. Finally, we discuss the possibility of predicting a signal solely from past samples using sampling series based on Gaussian generators.