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Subjects
43-XX Abstract harmonic analysis
43Axx Abstract harmonic analysis
43A45 Spectral synthesis on groups, semigroups, etc.

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Harmonic Analysis and Spectral Synthesis in Central Hypergroups.

Matthias Vogel (1988)

Mathematische Annalen

Harmonic synthesis for subgroups

Carl S. Herz (1973)

Annales de l'institut Fourier

Let $G$ be a locally compact group and $H$ a closed subgroup. Then $H$ is always a set of local spectral synthesis with respect to the algebra $A_{p} (G)$ , where $A_{2} (G)$ is the Fourier algebra in the sense of Eymard. Global synthesis holds if and only if a certain condition (C) is satisfied; it is whenever the subgroup $H$ is amenable or normal. Global synthesis implies that each convolution operator on $L^{p} (G)$ with support in $H$ which is the ultraweak limit of measures carried by $H$ . The problem of passing from local to global...

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