K-spherical representations for Gelfand pairs associated to solvable Lie groups

Katsuhiko KIKUCHI

doi:10.2969/jmsj/04930469

Katsuhiko KIKUCHI

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 3 Pages 469-486

DOI https://doi.org/10.2969/jmsj/04930469

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Published: 1997 Received: June 01, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : BJR) C. Benson, J. Jenkins and G. Ratcliff, On Gelfand pairs associated with solvable Lie groups, Trans. Amer. Math. Soc., 321 (1990), 85-116.
C) G. Carcano, A commutativity condition for algebras of invariant functions, Boll. Un. Mat. Italiano, 7 (1987), 1091-1105.
D) J. Dixmier, C^*-algebras, North-Holland, Amsterdam, 1977.
G1) J. Glimm, Type I C^*-algebras, Ann. Math., 73 (1961), 572-612.
G2) J. Glimm, Locally compact transformation groups, Trans. Amer. Math. Soc., 101 (1961), 124-138.
H) S. Helgason, Groups and Geometric Analysis, Academic Press, New York, 1984.
J) J. Jenkins, Growth of connected locally compact groups, J. Funct. Anal., 12 (1973), 113-127.
Ki) K. Kikuchi, On Gelfand pairs associated with nilpotent Lie groups, J. Math. Kyoto Univ., 34 (1994), 741-754.
Ku) M. Kuranishi, On non-connected maximally almost periodic groups, Tohoku Math. J., 2 (1950), 40-46.
L) J. Ludwig, A class of symmetric and a class of Wiener group algebras, J. Funct. Anal., 31 (1979), 187-194.
M) G. Mackey, Unitary representations of group extensions, I, Acta Math., 99 (1958), 265-311.
P) D. Poguntke, Nilpotente Liesche Gruppen haben symmetrische Gruppenalgebren, Math. Ann., 227 (1977), 51-59.

Right : [BJR] C. Benson, J. Jenkins and G. Ratcliff, On Gelfand pairs associated with solvable Lie groups, Trans. Amer. Math. Soc., 321 (1990), 85-116.
[C] G. Carcano, A commutativity condition for algebras of invariant functions, Boll. Un. Mat. Italiano, 7 (1987), 1091-1105.
[D] J. Dixmier, C^*-algebras, North-Holland, Amsterdam, 1977.
[G1] J. Glimm, Type I C^*-algebras, Ann. Math., 73 (1961), 572-612.
[G2] J. Glimm, Locally compact transformation groups, Trans. Amer. Math. Soc., 101 (1961), 124-138.
[H] S. Helgason, Groups and Geometric Analysis, Academic Press, New York, 1984.
[J] J. Jenkins, Growth of connected locally compact groups, J. Funct. Anal., 12 (1973), 113-127.
[Ki] K. Kikuchi, On Gelfand pairs associated with nilpotent Lie groups, J. Math. Kyoto Univ., 34 (1994), 741-754.
[Ku] M. Kuranishi, On non-connected maximally almost periodic groups, Tôhoku Math. J., 2 (1950), 40-46.
[L] J. Ludwig, A class of symmetric and a class of Wiener group algebras, J. Funct. Anal., 31 (1979), 187-194.
[M] G. Mackey, Unitary representations of group extensions, I, Acta Math., 99 (1958), 265-311.
[P] D. Poguntke, Nilpotente Liesche Gruppen haben symmetrische Gruppenalgebren, Math. Ann., 227 (1977), 51-59.

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