Quasi-projection operators in the weighted $L_p$ spaces

TL;DR

This paper investigates the approximation capabilities and convergence rates of multivariate quasi-projection operators, including sampling and Kantorovich-Kotelnikov types, in weighted $L_p$ spaces, especially for signals with limited decay.

Contribution

It provides new analysis of convergence rates for a broad class of quasi-projection operators in weighted $L_p$ spaces, extending understanding of signal reconstruction errors.

Findings

Established convergence rates in weighted $L_p$ spaces.

Included operators generated by various band-limited functions.

Provided error estimates for signals with limited decay.

Abstract

Approximation properties of multivariate quasi-projection operators are studied in the paper. Wide classes of such operators are considered, including the sampling and the Kantorovich-Kotelnikov type operators generated by different band-limited functions.The rate of convergence in the weighted $L_p$-spaces for these operators is investigated. The results allow to estimate the error for reconstruction of signals (approximated functions) whose decay is not enough to be in $L_p$.