On the Riesz Means of Expansion by Riesz Bases Formed by Eigen Functions for the Ordinary Differential Operator of 2mth Order

Abstract

The aim of this paper is to prove a theorem on the Riesz means of expansions with respect to Riesz bases, which extends the previous results of [1] and [2] on the Schrödinger operator and the ordinary differential operator of 4-th order to the operator of order 2m by using the eigen functions of the ordinary differential operator. Some Symbols that used in the paper: the uniform norm. the inner product in L2. G the set of all boundary elements of G. ˆ u the dual function of u.