Quasi-projection operators in the weighted $L_p$ spaces

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 $L_p$.