The plancherel formula for group extensions
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 5 (1972) no. 3, pp. 459-516.
@article{ASENS_1972_4_5_3_459_0,
     author = {Kleppner, Adam and Lipsman, Ronald},
     title = {The plancherel formula for group extensions},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {459--516},
     publisher = {Elsevier},
     volume = {Ser. 4, 5},
     number = {3},
     year = {1972},
     doi = {10.24033/asens.1235},
     mrnumber = {49 #7387},
     zbl = {0239.43003},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1235/}
}
TY  - JOUR
AU  - Kleppner, Adam
AU  - Lipsman, Ronald
TI  - The plancherel formula for group extensions
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1972
SP  - 459
EP  - 516
VL  - 5
IS  - 3
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.24033/asens.1235/
DO  - 10.24033/asens.1235
LA  - en
ID  - ASENS_1972_4_5_3_459_0
ER  - 
%0 Journal Article
%A Kleppner, Adam
%A Lipsman, Ronald
%T The plancherel formula for group extensions
%J Annales scientifiques de l'École Normale Supérieure
%D 1972
%P 459-516
%V 5
%N 3
%I Elsevier
%U http://archive.numdam.org/articles/10.24033/asens.1235/
%R 10.24033/asens.1235
%G en
%F ASENS_1972_4_5_3_459_0
Kleppner, Adam; Lipsman, Ronald. The plancherel formula for group extensions. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 5 (1972) no. 3, pp. 459-516. doi : 10.24033/asens.1235. http://archive.numdam.org/articles/10.24033/asens.1235/

[1] L. Auslander and C. Moore, Unitary representations of solvable Lie groups (Memoirs Amer. Math. Soc., No. 62, 1966). | MR | Zbl

[2] L. Baggett, A weak containment theorem for groups with a quotient R-group (Trans. Amer. Math. Soc., vol. 128, 1967, p. 277-290). | MR | Zbl

[3] N. Bourbaki, Intégration, chap. V, Hermann, Paris, 1956.

[4] N. Bourbaki, Intégration, chap. VI, Hermann, Paris, 1963.

[5] F. Bruhat, Sur les représentations induites des groupes de Lie (Bull. Soc. Math. Fr., vol. 84, 1956, p. 97-205). | Numdam | MR | Zbl

[6] E. Davies, On the Borel structure of C*-algebras (Comm. Math. Phys., vol. 8, 1968 p. 147-163). | MR | Zbl

[7] J. Dixmier, Algèbres quasi-unitaires (Comm. Math. Helv., vol. 26, 1952, p. 275-322). | MR | Zbl

[8] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris, 1957. | Zbl

[9] J. Dixmier, Sur les représentations des groupes de Lie nilpotents, III (Can. J. Math., vol. 10, 1958, p. 321-348). | MR | Zbl

[10] J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964. | MR | Zbl

[11] J. Dixmier, Sur la représentation régulière d'un groupe localement compact connexe (Ann. scient. Éc. Norm. Sup., vol. 2, 1969, p. 423-436). | Numdam | MR | Zbl

[12] E. Effros, The Borel space of von Neumann algebras on a separable Hilbert space (Pac. J. Math., vol. 15, 1965, p. 1153-1164). | MR | Zbl

[13] E. Effros, The canonical measures for a separable C*-algebra (Amer. J. Math., vol. 92, 1970, p. 56-60). | MR | Zbl

[14] J. Fell, Weak containment and induced representations of groups (Can. J. Math., vol. 14, 1962, p. 237-268). | MR | Zbl

[15] J. Glimm, Locally compact transformation groups (Trans. Amer. Math. Soc., vol. 101, 1961, p. 124-138). | MR | Zbl

[16] S. Grosser and M. Moskowitz, Harmonic Analysis on central topological groups (Trans. Amer. Math. Soc., vol. 156, 1971, p. 419-454). | MR | Zbl

[17] A. Guichardet, Caractères des algèbres de Banach involutives (Ann. Inst. Fourier, vol. 13, 1963, p. 1-81). | Numdam | MR | Zbl

[18] R. Kallman, Certain topological groups are type I (Bull. Amer. Math. Soc., vol. 76, 1970, p. 404-406). | MR | Zbl

[19] C. Kuratowski, Topologie, I, Warsaw, 1938.

[20] R. Lipsman, Uniformly bounded representations of the Lorentz groups (Amer. J. Math., vol. 91, 1969, p. 938-962). | MR | Zbl

[21] R. Lipsman, Representation theory of almost connected groups (Pac. J. Math., vol. 42, 1972) (to appear). | MR | Zbl

[22] G. Mackey, Induced representations of locally compact groups, I (Ann. of Math., vol. 55, 1952, p. 101-139). | MR | Zbl

[23] G. Mackey, Borel structures in groups and their duals (Trans. Amer. Math. Soc., vol. 85, 1957, p. 134-165). | MR | Zbl

[24] G. Mackey, Unitary representations of group extensions, I (Acta Math., vol. 99, 1958, p. 265-311). | MR | Zbl

[25] G. Mackey, Group representations and non-commutative harmonic analysis, University of California, Berkeley, 1965.

[26] C. Moore, Groups with finite-dimensional irreducible representations (Trans. Amer. Math. Soc., vol. 166, 1972, p. 401-410). | MR | Zbl

[27] C. Moore, A Plancherel formula for non-unimodular groups, Address presented to the International Conference on Harmonic Analysis, University of Maryland, November 1971.

[28] L. Pukanszky, On the theory of quasi-unitary algebras (Acta Sci. Math., vol. 16, 1955, p. 103-121). | MR | Zbl

[29] L. Pukanszky, Unitary representations of solvable Lie groups (Ann. scient. Éc. Norm. Sup., vol. 4, 1971, p. 457-608). | Numdam | MR | Zbl

[30] G. Rideau, On the reduction of the regular representation of the Poincaré group (Comm. Math. Phys., vol. 3, 1966, p. 218-227). | MR | Zbl

[31] N. Tatsuuma, Plancherel formula for non-unimodular locally compact groups (J. of Math. of Kyoto Univ., vol. 12, 1972, p. 179-261). | MR | Zbl

[32] V. Varadarajan, Groups of automorphism of Borel spaces (Trans. Amer. Math. Soc., vol. 109, 1963, p. 191-220). | MR | Zbl

Cited by Sources: