References
A. Erdelyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, 1953.
I. M. Gelfand and S. G. Gindikin, “Complex manifolds whose skeletons are semisimple real Lie groups and the holomorphic discrete series of representations,” Funkts. Anal. Prilozhen.,11, No. 4, 19–27 (1977).
I. M. Gelfand and G. E. Shilov, Generalized Functions and Operations on Them, Academic Press, New York, 1964.
V. F. Molchanov, “Analogue of the Plancherel formula for hyperboloids.,” Dokl. Akad. Nauk SSSR,183, No. 2, 288–291 (1968).
V. F. Molchanov, “Representations of a pseudo-orthogonal group associated with a cone,” Mat. Sb.,81, No. 3, 358–375 (1970).
V. F. Molchanov, “Spherical functions on hyperboloids,” Mat. Sb.,99 (141), No. 2, 139–161 (1976).
V. F. Molchanov, “The Plancherel formula for hyperboloids,” Trudy Mat. Inst. Steklov,147, 65–85 (1980).
V. F. Molchanov, “Quantization on the imaginary Lobachevsky plane,” Funkts. Anal. Prilozhen.,14, No. 2, 73–74 (1980).
V. F. Molchanov, “Harmonic analysis on homogeneous spaces,” in: Encycl. Math. Sci., Vol. 59, Springer, Berlin, 1995, pp. 1–135.
S. G. Gindikin, “Conformal analysis on hyperboloids,” J. Geom. Phys.,10, 175–184 (1993).
S. Matsumoto, “Discrete series for an affine symmetric space,” Hiroshima Math. J.,11, 53–79 (1981).
V. F. Molchanov, “Holomorphic discrete series for hyperboloids of Hermitian type,” J. Funct. Anal.,147, No. 1, 26–50 (1997).
G. Olafsson and B. Ørsted, “The holomorphic discrete series for affine symmetric spaces, I,” J. Funct. Anal.,81, No. 1, 126–159 (1988).
W. Rossmann, “Analysis on real hyperbolic spaces,” J. Funct. Anal.,30, No. 3, 448–477 (1978).
R. S. Strichartz, “Harmonic analysis on hyperboloids,” J. Funct. Anal.,12, No. 4, 341–383 (1973).
A. Tengstrand, “Distributions invariant under an orthogonal group of arbitrary signature,” Math. Scand.,8, 201–218 (1960).
Additional information
This research was partially supported by the RFBR under grant 94-01-01603-a and by the ISF and the Russian Government under grant JC 7100. A part of this research was performed during the author's stay at the Mittag-Leffler Institute in Djursholm, Sweden, in January–February 1996.
Tambov State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 31, No. 3, pp. 35–43, July–September, 1997.
Translated by V. F. Molchanov
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Molchanov, V.F. Separation of series for hyperboloids. Funct Anal Its Appl 31, 176–182 (1997). https://doi.org/10.1007/BF02465785
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DOI: https://doi.org/10.1007/BF02465785