A generalized Fourier transformation for L1(G)-Modules
1984 ◽
Vol 36
(3)
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pp. 365-377
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AbstractLet G be a compact abelian group with dual Ĝ and let K be a Banach L1 (G)-module. We introduce the notion of character convolution transformation of K which reduces to ordinary Fourier or Fourier-Stieltjes transformation when K is one of the spaces Lp(G), M(G). We show that the question of what maps Ĝ → K extend to multipliers of K is a question of asking for descriptions of the character convolution transforms. In this setting some results of Helson-Edward and Schoenberg-Eberlein find generalizations, as do some classical results, including the inversion formula and the Parseval relation. We then apply these results to transformation groups, obtaining a variant of a theorem of Bochner and an extension of a theorem of Ryan.
1994 ◽
Vol 14
(2)
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pp. 130-138
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2007 ◽
Vol 75
(2)
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pp. 369-390
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2008 ◽
Vol 340
(1)
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pp. 219-225
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1973 ◽
Vol 9
(1)
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pp. 73-82
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1984 ◽
pp. 261-269
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1995 ◽
Vol 58
(3)
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pp. 387-403
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