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Expansion of automorphic functions

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Abstract

This paper proposes a method of expansion for automorphic functions on Lie groups, which generalizes the usual Fourier series expansion of automorphic functions on SL2(ℝ)/SO(2). Detailed consideration is given to the special case of the expansion of functions on SL3(ℝ)/SO(3), which are automorphic with respect to SL3(ℤ).

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Literature cited

  1. N. Ya. Vilenkin, Special Functions and the Theory of Group Representations, Amer. Math. Soc., Providence (1968).

    Google Scholar 

  2. A. I. Vinogradov and L. A. Takhtadzhyan, “The theory of Eisenstein series for SL3(ℝ) and its application to a binary problem,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,76, 5–52 (1978).

    Google Scholar 

  3. I. M. Gel'fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Representation Theory and Automorphic Functions, W. B. Saunders, Philadelphia-London-Toronto (1969).

    Google Scholar 

  4. A. A. Kirillov, “Unitary representations of nilpotent Lie groups,” Usp. Mat. Nauk,17, No. 4, 57–110 (1962).

    Google Scholar 

  5. A. A. Kirillov, Elements of the Theory of Representations, Springer-Verlag, Berlin-Heidelberg-New York (1976).

    Google Scholar 

  6. G. I. Ol'shanskii, “The Frobenius reciprocity theorem,” Funkts. Anal.,3, No. 4, 49–58 (1969).

    Google Scholar 

  7. J. Dixmier, “Sur les représentations unitaires des groupes de Lie nilpotents. II,” Bull. Soc. Math. France,85, 325–388 (1957).

    Google Scholar 

  8. J. Dixmier, “Sur les représentations unitaires des groupes de Lie nilpotents. III,” Can. J. Math.,10, No. 3, 321–348 (1958).

    Google Scholar 

  9. Harish-Chandra, “Representations of a semisimple Lie group on a Banach space. I,” Trans. Am. Math. Soc.,75, No. 2, 185–243 (1953).

    Google Scholar 

  10. Harish-Chandra, “Automorphic forms on semisimple Lie groups,” Lect. Notes Math.,62, Springer-Verlag, Berlin-Heidelberg-New York (1968).

    Google Scholar 

  11. R. P. Langlands, “On the functional equations satisfied by Eisenstein series,” Lect. Notes Math.,544, Springer-Verlag, Berlin-Heidelberg-New York (1976).

    Google Scholar 

  12. C. C. Moore, “Decomposition of unitary representations defined by discrete subgroups of nilpotent groups,” Ann. Math.,82, No. 1, 146–182 (1965).

    Google Scholar 

  13. J. von Neumann, “Die Eindeutigkeit der Schrödingerschen Operadtren,” Math. Ann.,104, 570–578 (1931).

    Google Scholar 

  14. A. Selberg, “Discontinuous groups and harmonic analysis,” Int. Congr. Math. Stockholm (1962), pp. 177–189.

  15. M. H. Stone, “Linear transformations in Hilbert space. III. Operational methods and group theory,” Proc. Nat. Acad. Sci. USA (1930), p. 16.

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Authors
  1. N. V. Proskurin
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 119–141, 1982.

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Proskurin, N.V. Expansion of automorphic functions. J Math Sci 26, 1908–1921 (1984). https://doi.org/10.1007/BF01670579

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  • DOI: https://doi.org/10.1007/BF01670579

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