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Acta Mathematica Vietnamica

VOLTERRA RIGHT INVERSES FOR WEIGHTED DIFFERENCE OPERATORS IN LINEAR SPACES

NGUYEN VAN MAU, NGUYEN VU LUONG

Abstract

Let X be a linear space over a field F of scalars and let Xω be the set of all infinite sequences x=(x0,x1,), where xjX. Let  A=(A0,A1,) be a sequence in L0(X). Consider the weighted difference operator in Xω:DAx=(xn+1Anxn). 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 DA. 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.