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On the synthesis problem for orbits of Lie groups in \(R^ n\). (English) Zbl 0478.43004


MSC:

43A45 Spectral synthesis on groups, semigroups, etc.
43A70 Analysis on specific locally compact and other abelian groups
22B10 Structure of group algebras of LCA groups

Citations:

Zbl 0212.150
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References:

[1] Domar, Y., On the spectral synthesis problem for (n−1)-dimensional subsets ofR^n, Ark. Mat., 9, 23-37 (1971) · Zbl 0212.15004 · doi:10.1007/BF02383635
[2] Domar, Y., AC^∞-curve of spectral non-synthesis, Mathematika, 24, 189-192 (1977) · Zbl 0366.43004 · doi:10.1112/S0025579300009098
[3] Helgason, S.,Differential Geometry and Symmetric Spaces. New York, 1962. · Zbl 0111.18101
[4] Herz, C. S., Spectral synthesis for the circle, Ann. of Math., 68, 709-712 (1958) · Zbl 0084.09703 · doi:10.2307/1970163
[5] Hochschild, G.,The structure of Lie groups. San Francisco, 1965. · Zbl 0131.02702
[6] Leptin, H., Lokalkompakte Gruppen mit symmetrischen Algebren, Symposia Math., 22, 267-281 (1977) · Zbl 0394.43003
[7] Littman, W., Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc., 69, 766-770 (1963) · Zbl 0143.34701 · doi:10.1090/S0002-9904-1963-11025-3
[8] Lust, F., Le probleme de la synthese et de lap-finesse pour certain orbites des groupes lineares dansA_p(R^n), Studia Math., 39, 17-28 (1971) · Zbl 0231.43008
[9] Reiter, H.,Classical harmonic analysis and locally compact groups. Oxford, 1968. · Zbl 0165.15601
[10] Schwartz, L.,Theorie des distributions. Paris, 1966. · Zbl 0149.09501
[11] Varopoulos, N. Th., Spectral synthesis on spheres, Proc. Cambridge Phil. Soc., 62, 379-387 (1966) · Zbl 0154.39204 · doi:10.1017/S0305004100039967
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