Abstract
Abstract : Given a locally compact Abelian group and the space integrable functions on said group; with the space of multipliers on the functions defined as the space of bounded operators on the functions which commute with translations by elements of the group; it is proved that the space of multipliers is the conjugate space of a Banach space of continuous functions on the group. As a direct consequence, it is shown that the space of multipliers is the closure in the weak (strong) operator topology of the span of the translation operators. The results are applied to the study of translates of multipliers and to the relations between multipliers and lacunary sets of the character group of the compact group. (Author)
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