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On Vector Valued Periodic Distributions

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Author(s): Gaşpar Păstorel | Nădăban Sorin | Sida Lavinia

Journal: Theory and Applications of Mathematics & Computer Science
ISSN 2067-2764

Volume: 2;
Issue: 1;
Start page: 1;
Date: 2012;
Original page

Keywords: Periodic functions | periodic distributions | vector valued periodic distributions

ABSTRACT
In this paper we consider vector valued (X-valued with X a Banach space) distributions on the euclidean space Rd, extending the T-periodicity, and the T-periodic transform with T = (T1, …,Td) € Rd, Ti > 0 from the scalar case to the Banach space valued case.Besides immediate basic properties of these concepts, a realization of the space of X-valued T-periodic distributions, up to a toplinear isomorphism, as the space of all bounded linear operators from the space of T-periodic test functions to the Banach space X is given.
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