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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Neocontinuous Mikusiński operators

Authors: Carl C. Hughes and Raimond A. Struble
Journal: Trans. Amer. Math. Soc. 185 (1973), 383-400
MSC: Primary 46FXX; Secondary 44A40
MathSciNet review: 0333719
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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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Keywords: Mikusiński operator, distribution, operational calculus, convolution ring, ideal, field of operators, representation, module homomorphism, continuity, linear space, linear transformation, partial differential operator
Article copyright: © Copyright 1973 American Mathematical Society