A characterization of compact multipliers

Authors:
Gregory F. Bachelis and Louis Pigno

Journal:
Trans. Amer. Math. Soc. **165** (1972), 319-322

MSC:
Primary 43A22; Secondary 43A25

DOI:
https://doi.org/10.1090/S0002-9947-1972-0300012-X

MathSciNet review:
0300012

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Abstract: Let *G* be a compact abelian group and a complex-valued function defined on the dual . The main result of this paper is that is a compact multiplier of type and , if and only if it satisfies the following condition: Given there corresponds a finite set such that whenever and are trigonometric polynomials satisfying ( the conjugate index of *q*) and for . Using the above characterization we obtain the following necessary and sufficient condition for to be the Fourier transform of a continuous complex-valued function on *G*: Given there corresponds a finite set such that whenever is a trigonometric polynomial satisfying and for .

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DOI:
https://doi.org/10.1090/S0002-9947-1972-0300012-X

Article copyright:
© Copyright 1972
American Mathematical Society