×

La transformation de Fourier-Plancherel analytique des groupes de Lie. II: Les groupes nilpotents. (French) Zbl 0498.43009


MSC:

43A80 Analysis on other specific Lie groups
22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
PDFBibTeX XMLCite
Full Text: DOI Numdam EuDML

References:

[1] [1] & Fourier Transform of smooth functions on certain Nilpotent Lie groups, Jour. Funct. Anal., 37 (1980), 203-217. · Zbl 0456.43006
[2] [2] Algèbres enveloppantes, Gauthier-Villars, Paris, 1974. · Zbl 0308.17007
[3] [3] A connection between Nilpotent Lie Groups and Oscillatory integrals associated to singularities, Pacific Jour. Math., 73 (1977), 329-364. · Zbl 0383.22009
[4] [4] & Sur les corps liés aux algèbres enveloppantes, Publ. Math. IHES, n° 31 (1966), 5-20. · Zbl 0144.02104
[5] [5] , La Transformation de Fourier-Plancherel analytique des groupes de Lie. I. Algèbres de Weyl et opérateurs différentiels, Ann. Inst. Fourier, 33-4 (1983), 95-133. · Zbl 0498.43008
[6] [6] Une variante de la conjecture de Gelfand-Kirillov et la Transformation de Fourier-Plancherel. C.R.A.S., Paris, tome 293, série 1, p. 381-384. · Zbl 0472.43008
[7] [7] Construction analytique de la Transformation de Fourier-Plancherel des groupes de Lie. Cours de 3è Cycle Orsay, Université de Paris-Sud (1979), Publ. Math. Orsay, (1979) n° 79.06. · Zbl 0477.43011
[8] [8] Algèbres de Heisenberg et géométrie symplectique des algèbres de Lie, Publ. Math. Orsay (1978) n° 78.08. · Zbl 0392.17007
[9] [9] Harmonic analysis on the Poincaré Group :
[10] [ManPa] ,
[11] II. The Fourier Transform, Comm. Math. Phys., 22 (1971), 301-320. · Zbl 0221.43015
[12] [10] Sur certaines représentations d’une algèbre de Lie résoluble complexe (I), Bull. Sc. Math., 97 (1973), 105-128. · Zbl 0275.17003
[13] [11] Unitary representations of nilpotent Lie Groups, Uspekhi Math. Nauk., 17 (1962), 57-110. · Zbl 0106.25001
[14] [12] Leçons sur les représentations des groupes, Dunod, Paris, 1967. · Zbl 0152.01201
[15] [13] Unitary representations of solvable Lie Groups, Ann. Sci. Ec. Norm. Sup., 4è Série, 4 (1971), 457-608. · Zbl 0238.22010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.