On Generalized Sampling Series

A. Sathish Kumar, Puja Sonawane

Session: Sampling and learning of deep neural networks (Philipp Petersen)

Keywords: Generalized Sampling Series, Kantorovich Sampling Series, Degree of Approximation, Modulus of Smoothness, Log-H$\ddot{o}$lderian Class.

TL;DR: Analysing the approximation error by generalised sampling series.

Abstract: In the present paper, we analyse the approximation behaviour of generalized sampling series and Kantorovich sampling series. First, we obtain the approximation error in-terms of the modulus of continuity for the generalized sampling series for functions in $C(\mathbb{R}^{d}).$ Further, for the class of log-H$\ddot{o}$lderian functions, the order of uniform norm convergence is discussed. Furthermore, for functions in $C(\mathbb{R}^{d})$ and log-H$\ddot{o}$lderian functions, we provide the approximation error for the Kantorovich sampling series.

Submission Number: 41