Approximation properties of periodic multivariate quasi-interpolation operators

We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions (phi) over tilde (j) and trigonometric polynomials and trigonometric polynomials phi(j). The class of such operators includes classical interpolation polynomials ((phi) over tilde (j) is the Dirac delta function), Kantorovich-type operators ((phi) over tilde (j) is a characteristic function), scaling expansions associated with wavelet constructions, and others. Under different compatibility conditions on (phi) over tilde (j )and phi(j), we obtain upper and lower bound estimates for the L-p-error of approximation by quasi-interpolation operators in terms of the best and best one-sided approximation, classical and fractional moduli of smoothness, K-functionals, and other terms. (C) 2021 Elsevier Inc. All rights reserved.