The Central Approximation Theorems for the Method of Left Gamma Quasi-Interpolants in L p spaces

Abstract

The optimal degree of approximation of the method of Gammaoperators G n in L p spaces is O(n -1). In order to obtain much faster convergence, quasi-interpolants G n (k) of G n in the sense of Sablonniere are considered. We show that for fixed k the operator-norms ∥G n (k) ∥p are uniformly bounded in n. In addition to this, for the first time in the theory of quasi-interpolants, all central problems for approximation methods (direct theorem, inverse theorem, equivalence theorem) could be solved completely for the L p metric. Left Gamma quasi-interpolants turn out to be as powerful as linear combinations of Gammaoperators [6].