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Functional Equations, Distributions and Approximate Identities

Published online by Cambridge University Press:  20 November 2018

John A. Baker
John A. Baker*
Affiliation:
University of Waterloo, Waterloo, OntarioCanada N2L 3G1
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The subject of this paper is the use of the theory of Schwartz distributions and approximate identities in studying the functional equation

The aj’s and b are complex-valued functions defined on a neighbourhood, U, of 0 in Rm, hj. U → Rn with hj(0) = 0 and fj, g: Rn → C for 1 ≦ j ≦ N. In most of what follows the aj's and hj's are assumed smooth and may be thought of as given. The fj‘s, b and g may be thought of as the unknowns. Typically we are concerned with locally integrable functions f1, … , fN such that, for each s in U, (1) holds for a.e. (almost every) x ∈ Rn, in the sense of Lebesgue measure.

Keywords

39B2039B3039B4046F99
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 4 , 01 August 1990 , pp. 696 - 708
Copyright
Copyright © Canadian Mathematical Society 1990

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