Vol. 37, No. 1, 1971

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The abstract Goursat problem

Hector O. Fattorini

Vol. 37 (1971), No. 1, 51–83

Let Dα be a differential monomial in n variables. We try to identify in this paper those closed, densely defined linear operators A (in a fairly general class of locally convex spaces) such that the equation (Dα A)S = δ I has a solution; here S is an operator-valued distribution in n variables with support in the cone of nonnegative coordinates. The results are applied to the study of the equation (Dα A)U = T,T a distribution with values in the space where A is defined, and to the formulation and solution of an “abstract Goursat problem” that reduces to the abstract Cauchy problem when

n = 1.

Mathematical Subject Classification 2000
Primary: 47D05
Secondary: 35R99, 34G05
Received: 20 January 1970
Published: 1 April 1971
Hector O. Fattorini