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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.)
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References:

[1] L. CORWIN & F.P. GREENLEAFFourier transform of smooth functions on certain nilpotent Lie groups, Jour. Funct. Anal., 37 (1980), 203-217. · Zbl 0456.43006
[2] J. DIXMIERAlgèbres enveloppantes, Gauthier-Villars, Paris, 1974. · Zbl 0308.17007
[3] R.E. HOWEA connection between nilpotent Lie groups and oscillatory integrals associated to singularities, Pacific Jour. Math., 73 (1977), 329-364. · Zbl 0383.22009
[4] I.M. GELFAND & A.A. KIRILLOVSur LES corps liés aux algèbres enveloppantes, Publ. Math. IHES, n° 31 (1966), 5-20. · Zbl 0144.02104
[5] NGHIÊM XUÂN HAI, 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
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[7] NGHIÊM XUÂN HAIConstruction 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] NGHIÊM XUÂN HAIAlgèbres de Heisenberg et géométrie symplectique des algèbres de Lie, Publ. Math. Orsay (1978) n° 78.08. · Zbl 0392.17007
[9] NGHIÊM XUÂN HAIHarmonic analysis on the Poincaré group :
[10] I. Generalized matrix elements, Comm. Math. Phys., 12 (1969), 331-350.
[11] II. The Fourier transform, Comm. Math. Phys., 22 (1971), 301-320. · Zbl 0221.43015
[12] NGHIÊM XUÂN HAISur certaines représentations d’une algèbre de Lie résoluble complexe (I), Bull. Sc. Math., 97 (1973), 105-128. · Zbl 0275.17003
[13] A.A. KIRILLOVUnitary representations of nilpotent Lie groups, Uspekhi Math. Nauk., 17 (1962), 57-110. · Zbl 0106.25001
[14] L. PUKANSZKYLeçons sur LES représentations des groupes, Dunod, Paris, 1967. · Zbl 0152.01201
[15] L. PUKANSZKYUnitary representations of solvable Lie groups, Ann. Sci. Ec. Norm. Sup., 4è Série, 4 (1971), 457-608. · Zbl 0238.22010
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