An algebra of distributions on an open interval
Author:
Harris S. Shultz
Journal:
Trans. Amer. Math. Soc. 169 (1972), 163-181
MSC:
Primary 46F05
DOI:
https://doi.org/10.1090/S0002-9947-1972-0308775-4
MathSciNet review:
0308775
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be any open subinterval of the reals which contains the origin and let
denote the family of all distributions on
which are regular in some interval
, where
. Then
is a commutative algebra: Multiplication is defined so that, when restricted to those distributions on
whose supports are contained in
, it is ordinary convolution. Also,
can be injected into an algebra of operators; this family of operators is a sequentially complete locally convex space. Since it preserves multiplication, this injection serves as a generalization (there are no growth restrictions) of the two-sided Laplace transformation.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1972-0308775-4
Keywords:
Generalized functions,
operational calculus,
Schwartz distributions,
two-sided Laplace transformation,
Fourier transformation
Article copyright:
© Copyright 1972
American Mathematical Society