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Abstract Plancherel theorems and a Frobenius reciprocity theorem. (English) Zbl 0305.22016


MSC:

22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
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References:

[1] Blattner, R. T., On induced representations, Amer. J. Math., 83, 79-98 (1961) · Zbl 0122.28405
[2] Cartier, P., Quantum mechanical commutation relations and theta functions, (Boulder Symposium on Algebraic Groups and Discontinuous Subgroups (1966), Amer. Math. Soc: Amer. Math. Soc Providence), 361-383 · Zbl 0178.28401
[3] Gelfand, I. M.; Pyateckii-Sapiro, I. I., Uspehi Mat. Nauk, 14, No. 3 (87), 3-19 (1959), (N.S.) · Zbl 0091.08805
[4] Goodman, R., Complex Fourier analysis on nilpotent Lie groups, Trans. Amer. Math. Soc., 160, 373 (1971) · Zbl 0225.22018
[5] Kleppner-Lipsman; Kleppner-Lipsman · Zbl 0239.43003
[6] Mackey, G. W., Induced representations of locally compact groups and applications, (Conference on Functional Analysis and Related Fields (1970), Springer-Verlag: Springer-Verlag New York) · Zbl 0216.39904
[7] Moore, C. C., Representations of solvable and nilpotent groups and harmonic analysis on nil and solvmanifolds, (Address presented to the “Conference on Harmonic Analysis on Homogeneous Spaces”. Address presented to the “Conference on Harmonic Analysis on Homogeneous Spaces”, Williamstown, Massachusetts (1972)) · Zbl 0292.22015
[8] von Neumann, J., On rings of operators, III, Ann. Math., 41, 94-116 (1940) · Zbl 0023.13303
[9] Poulsen, N. S., On \(C^∞\)-vectors and intertwining bilinear forms for representations of Lie group, J. Functional Analysis, 9, 87-120 (1972) · Zbl 0237.22013
[10] Pukanszky, L., Representations of solvable Lie groups, Ann. Sci. École Norm. Sup., 4, 464-608 (1971) · Zbl 0238.22010
[11] Richardson, L. F., Decomposition of the \(L^2\) space of a general compact nilmanifold, Am. J. Math., 93, 173-190 (1971) · Zbl 0265.43012
[12] Steinspring, W. F., Integrability of Fourier transforms for unimodular Lie groups, Duke Math. J., 26, 123-131 (1959) · Zbl 0085.10301
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