Operator norms of Gauss-Weierstrass operators and their left quasi interpolants

Abstract

The paper deals with the Gauß-Weierstraß operators Wn and their left quasi interpolants W [r]n . The quasi interpolants were defined by Paul Sablonnière in 2014. Recently, their asymptotic behaviour was studied by Octavian Agratini, Radu Pȃltȃnea and the author by presenting complete asymptotic expansions. In this paper we derive estimates for the operator norms of Wn and W [r] n when acting on various function spaces. Mathematics Subject Classification (2010): 41A36, 41A45, 47A30. Keywords: Approximation by positive operators, operator norm.In the particular case c = 0, we obtain the ordinary spaces L p 0 (R) = L p (R) and L ∞ 0 (R) = L ∞ (R), respectively.