Set of uniqueness on noncommutative locally compact groups

Bożejko, Marek

doi:10.1090/S0002-9939-1977-0467174-5

Set of uniqueness on noncommutative locally compact groups
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Proc. Amer. Math. Soc. 64 (1977), 93-96 Request permission

Abstract:

Using the terminology of P. Eymard we adapt the notion of set of uniqueness to noncommutative case and we show that every compact and residual set in a locally compact nondiscrete group is a set of uniqueness.

References

N. K. Bari, Trigonometricheskie ryady, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961 (Russian). With the editorial collaboration of P. L. Ul′janov. MR 0126115
Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628, DOI 10.24033/bsmf.1607
Jean-Pierre Kahane and Raphaël Salem, Ensembles parfaits et séries trigonométriques, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1301, Hermann, Paris, 1963 (French). MR 0160065
L. H. Loomis, The spectral characterization of a class of almost periodic functions, Ann. of Math. (2) 72 (1960), 362–368. MR 120502, DOI 10.2307/1970139
Yves Meyer, Algebraic numbers and harmonic analysis, North-Holland Mathematical Library, Vol. 2, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1972. MR 0485769
Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
N. Th. Varopoulos, Sets of multiplicity in locally compact abelian groups, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 2, 123–158 (English, with French summary). MR 212508, DOI 10.5802/aif.238
A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587