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ZONAL AND ASSOCIATED FUNCTIONS ON SO0 p; q GROUPS

Year 2018, Volume: 8 Issue: 1, 32 - 43, 01.06.2018

Abstract

Explicit expressions for associated spherical functions of SO p; q matrix groups are obtained using a generalized hypergeometric series of two variables. In this paper we present explicit expressions for zonal functions of de Sitter groups and the group of conformal invariance. Moreover, we present a theorem on the transformation of derivative of distributions, concentrated on smooth surfaces, with respect to in nite- dimensional Lie group C1 Rn ;GL n .

References

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  • Theoretico-group methods in physics. Trudi mejd. semin. v Zveinigorode. - Moscow, ”Nauka”, v. 1-2 (1983) pp. 499-505. (in Russian).
  • Vilenkin N.Ya. Special functions and the theory of groups representations.- Moscow, ”Nauka”, (1991). (in Russian).
  • A.U. Klimik, Matrix elements and Clebsh-Gordon coefficients of group representations.-Kiev, ”Naukovo dumka”, (1979). (in Russian).
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  • I.M. Gelfand, G.E. Shilov, Generalized functions and operations on them, v.1,(1959) (in Russian).
  • F. Riordan, An introduction to combinatorial analysis, (1958), London, Chapman and Hall.
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  • A.N. Leznov, M. V. Saveliev, Preprint 72-3, Serpukhov, (1972).
Year 2018, Volume: 8 Issue: 1, 32 - 43, 01.06.2018

Abstract

References

  • A.O. Barut, R. Raczka, (1977), Theory of Group Representations and Applications, Warszawa.
  • Theoretico-group methods in physics. Trudi mejd. semin. v Zveinigorode. - Moscow, ”Nauka”, v. 1-2 (1983) pp. 499-505. (in Russian).
  • Vilenkin N.Ya. Special functions and the theory of groups representations.- Moscow, ”Nauka”, (1991). (in Russian).
  • A.U. Klimik, Matrix elements and Clebsh-Gordon coefficients of group representations.-Kiev, ”Naukovo dumka”, (1979). (in Russian).
  • C.S. Herz, Ann. of Math., 61, N3 (1955), pp. 474-523.
  • B.A. Rajabov, Proc. Nat. Acad. Sci., Azerbaijan, 44, N5 (1988), pp. 48-52; (in Russian).
  • B.A. Rajabov, Proc. Nat. Acad. Sci., Azerbaijan, 44, N7 (1988), pp.21-25; (in Russian).
  • B.A. Rajabov, Tr. J. of Physics, 18 (1994), 590 - 599.
  • Rajabov B.A.,(2003) arXiv:math-ph/0302051, p.6.
  • Rajabov B.A.,(2003) arXiv:math-ph/0303058, p.10.
  • Slater L.J. Generalized hypergeometric functions, (1966), Cambridge.
  • Treves F.,Topological Vector Spaces, Distributions and Kernels, (1967), Purdue University, Lafayette, Indiana.
  • I.M. Gelfand, G.E. Shilov, Generalized functions and operations on them, v.1,(1959) (in Russian).
  • F. Riordan, An introduction to combinatorial analysis, (1958), London, Chapman and Hall.
  • J. Horn, Math. Ann., 34, 544 (1889).
  • A.N. Leznov, M. V. Saveliev, Preprint 72-3, Serpukhov, (1972).
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

B.a. Rajabov This is me

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 1

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