Neocontinuous Mikusiński operators

Hughes, Carl C.; Struble, Raimond A.

doi:10.1090/S0002-9947-1973-0333719-X

Neocontinuous Mikusiński operators
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by Carl C. Hughes and Raimond A. Struble PDF

Trans. Amer. Math. Soc. 185 (1973), 383-400 Request permission

Abstract:

A class of Mikusiński-type operators in several variables, called neocontinuous operators, is studied. These particular operators are closely affiliated with Schwartz distributions on ${R^k}$ and share certain continuity properties with them. This affiliation is first of all revealed through a common algebraic view of operators and distributions as homomorphic mappings and a new representation theory, and is then characterized in terms of continuity properties of the mappings. The traditional procedures of the operational calculus apply to the class of neocontinuous operators. Moreover, the somewhat vague association of operational and distributional solutions of partial differential equations is replaced by the decisive representation concept, thus illustrating the appropriateness of the study of neocontinuous operators.

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