On the Schwartz-Bruhat space and the Paley-Wiener theorem for locally compact Abelian groups. (English) Zbl 0295.43008
MSC:
| 43A25 | Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups |
| 22B10 | Structure of group algebras of LCA groups |
| 43A15 | \(L^p\)-spaces and other function spaces on groups, semigroups, etc. |
| 26A12 | Rate of growth of functions, orders of infinity, slowly varying functions |
References:
| [1] | Bruhat, F., Distributions sur un groupe localement compact et applications à l’étude des représentations des groupes \(p\)-adiques, Bull. Soc. Math. France, 89, 43-75 (1961) · Zbl 0128.35701 |
| [2] | Rudin, W., Fourier Analysis on Groups, (Tracts in Mathematics, No. 12 (1962), Interscience: Interscience New York) · Zbl 0107.09603 |
| [3] | Warner, G., Harmonic Analysis on Semisimple Lie Groups I, (Die Grundlehren der Mathematischen Wissenschaften, band 188 (1972), Springer-Verlag: Springer-Verlag New York) · Zbl 0265.22020 |
| [4] | Weil, A., Sur certain groupes d’opérateurs unitaires, Acta Math., 111, 143-211 (1964) · Zbl 0203.03305 |
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