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Acta Mathematica

, Volume 139, Issue 1, pp 185–216 | Cite as

Unitary representations defined by boundary conditions—the case of sl(2,R)

  • R. Ranga Rao
Article

Keywords

Boundary Condition Unitary Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1].
    Bargmann, V., Irreducible unitary representations of the Lorentz group.Ann. of Math., (2) 48 (1947), 568–640.CrossRefMATHMathSciNetGoogle Scholar
  2. [2].
    Dunford, N. &Schwartz, J.,Linear operators, Part II. John Wiley, Interscience, New York, 1965.Google Scholar
  3. [3].
    Erdelyi, A., et al.,Higher transcendental functions, Vol. I. McGraw-Hill, New York, 1953.Google Scholar
  4. [4].
    —, et al.,Tables of integral transforms, Vol. I–II. McGraw-Hill, New York, 1953.Google Scholar
  5. [5].
    Gelfand, I. M. &Shilov, G. E.,Generalized functions,Vol. I. Academic Press, New York, 1964.Google Scholar
  6. [6].
    Kunze, R. A. &Stein, E. M., Uniformly bounded representations and harmonic analysis of the 2×2 real modular group.Amer. J. Math., 82 (1960), 1–62.MathSciNetGoogle Scholar
  7. [7].
    Narashimhan, R.,Analysis on real and complex manifolds. North-Holland Publishing Co., Amsterdam, 1968.Google Scholar
  8. [8].
    E. Nelson, Analytic vectors.Ann. of Math., (2), 70 (1959), 572–615.CrossRefMATHMathSciNetGoogle Scholar
  9. [9].
    Nelson, E. &Steinspring, W. F., Representation of elliptic operators in an enveloping algebra.Amer. J. Math., 81 (1959), 547–560.MathSciNetGoogle Scholar
  10. [10].
    Pukhansky, L., The Plancheral formula for the universal covering group ofSL(2,R).Math. Ann., 156 (1964), 96–143.CrossRefMathSciNetGoogle Scholar
  11. [11].
    Rallis, R. & Schiffmann, G., Weil Representation, I. Intertwining distributions and discrete spectrum. Preprint.Google Scholar
  12. [12].
    Ranga Rao, R., A reduction theory of g-modules and applications. In preparation.Google Scholar
  13. [13].
    Ranga Rao, R. On the decomposition of the Weil representation associated to a quadratic form. In preparation.Google Scholar
  14. [14].
    Sally, P. J., Analytic continuation of the irreducible unitary representations of the universal covering group ofSL (2,R).Mem. Amer. Math. Soc., 69 (1967).Google Scholar
  15. [15].
    Szegö, G.,Orthogonal polynomials. Revised ed., Amer. Math. Soc. Coll. Pub., Vol. 23, Providence, 1959.Google Scholar
  16. [16].
    Vilenkin, N. J.,Special functions and the theory of group representations. Amer. Math. Soc. Trans., 1968.Google Scholar
  17. [17].
    Warner, G.,Harmonic analysis on semi-simple Lie group, Vol. I. Springer-Verlag, 1972.Google Scholar

Copyright information

© Almqvist & Wiksell 1977

Authors and Affiliations

  • R. Ranga Rao
    • 1
  1. 1.University of IllinoisUrbanaUSA

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