Vol. 32, No. 1, 1970

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On a class of differential equations for vector-valued distributions

Hector O. Fattorini

Vol. 32 (1970), No. 1, 79–104
Abstract

The aim of this paper is to seek necessary and sufficient conditions on the linear operator A in a linear topological space in order that the Cauchy problem for the equation U(α) AU = T should be well set in the sense of distributions (see definition in §2). Here 0 < α < ,U(α) is the fractional derivative of U of order α. Such conditions are obtained for α integer 3 and then for any α > 0, this time with the additional assumption of (at most) exponential growth of the solutions at infinity.

Mathematical Subject Classification 2000
Primary: 35R99
Secondary: 47D05
Milestones
Received: 1 July 1968
Revised: 28 October 1968
Published: 1 January 1970
Authors
Hector O. Fattorini