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

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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