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- W2605772381 abstract "Let E be a closed subset of a locally compact Abelian group Г and let k(E) be the space of absolutely convergent Fourier transforms on Г that vanish on E. (1) k(E) is characterized as an ideal of arithmetic means defined by the behavior of pseudo-measures at infinity; and so spectral synthesis holds for an ideal I if I and its corresponding ideal of arithmetic means coincide. (2) We then prove that it is possible to synthesize pseudomeasures at infinity in a manner that runs parallel to Beurling's synthesis of weighted spaces. These two results are closely related by the notion of Wiener's spectrum." @default.
- W2605772381 created "2017-04-28" @default.
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- W2605772381 date "1975-06-01" @default.
- W2605772381 modified "2023-09-25" @default.
- W2605772381 title "The Wiener Spectrum in Spectral Synthesis" @default.
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- W2605772381 doi "https://doi.org/10.1002/sapm197554291" @default.
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