VOLTERRA RIGHT INVERSES FOR WEIGHTED DIFFERENCE OPERATORS IN LINEAR SPACES
NGUYEN VAN MAU, NGUYEN VU LUONG
Abstract
Let be a linear space over a field of scalars and let be the set of all infinite sequences , where . Let be a sequence in . Consider the weighted difference operator in . The scalar cases of weighted difference operators have been investigated, among others, by Przeworska-Rolewicz [3] and Kalfat [6]. In this paper we describe the set of all right inverses and the set of all initial operators for . Properties of fundamental right inverses and fundamental initial operators are studied. In particular, we give conditions for a fundamental right inverse to be Volterra and apply this result to solve the corresponding initial value problem.