Approximation properties of periodic multivariate quasi-interpolation operators

Yurii Kolomoitsev*, Jürgen Prestin

*Corresponding author for this work
2 Citations (Scopus)


We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions φ˜j and trigonometric polynomials φj. The class of such operators includes classical interpolation polynomials (φ˜j is the Dirac delta function), Kantorovich-type operators (φ˜j is a characteristic function), scaling expansions associated with wavelet constructions, and others. Under different compatibility conditions on φ˜j and φj, we obtain upper and lower bound estimates for the Lp-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.

Original languageEnglish
Article number105631
JournalJournal of Approximation Theory
Publication statusPublished - 10.2021


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