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Separation of series for hyperboloids

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References

  1. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, 1953.

    Google Scholar 

  2. 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).

    MATH  MathSciNet  Google Scholar 

  3. I. M. Gelfand and G. E. Shilov, Generalized Functions and Operations on Them, Academic Press, New York, 1964.

    Google Scholar 

  4. V. F. Molchanov, “Analogue of the Plancherel formula for hyperboloids.,” Dokl. Akad. Nauk SSSR,183, No. 2, 288–291 (1968).

    MATH  MathSciNet  Google Scholar 

  5. V. F. Molchanov, “Representations of a pseudo-orthogonal group associated with a cone,” Mat. Sb.,81, No. 3, 358–375 (1970).

    MATH  MathSciNet  Google Scholar 

  6. V. F. Molchanov, “Spherical functions on hyperboloids,” Mat. Sb.,99 (141), No. 2, 139–161 (1976).

    MATH  MathSciNet  Google Scholar 

  7. V. F. Molchanov, “The Plancherel formula for hyperboloids,” Trudy Mat. Inst. Steklov,147, 65–85 (1980).

    MATH  MathSciNet  Google Scholar 

  8. V. F. Molchanov, “Quantization on the imaginary Lobachevsky plane,” Funkts. Anal. Prilozhen.,14, No. 2, 73–74 (1980).

    MATH  MathSciNet  Google Scholar 

  9. V. F. Molchanov, “Harmonic analysis on homogeneous spaces,” in: Encycl. Math. Sci., Vol. 59, Springer, Berlin, 1995, pp. 1–135.

    Google Scholar 

  10. S. G. Gindikin, “Conformal analysis on hyperboloids,” J. Geom. Phys.,10, 175–184 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Matsumoto, “Discrete series for an affine symmetric space,” Hiroshima Math. J.,11, 53–79 (1981).

    MATH  MathSciNet  Google Scholar 

  12. V. F. Molchanov, “Holomorphic discrete series for hyperboloids of Hermitian type,” J. Funct. Anal.,147, No. 1, 26–50 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  13. G. Olafsson and B. Ørsted, “The holomorphic discrete series for affine symmetric spaces, I,” J. Funct. Anal.,81, No. 1, 126–159 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  14. W. Rossmann, “Analysis on real hyperbolic spaces,” J. Funct. Anal.,30, No. 3, 448–477 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  15. R. S. Strichartz, “Harmonic analysis on hyperboloids,” J. Funct. Anal.,12, No. 4, 341–383 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  16. A. Tengstrand, “Distributions invariant under an orthogonal group of arbitrary signature,” Math. Scand.,8, 201–218 (1960).

    MATH  MathSciNet  Google Scholar 

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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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