On two formulas for Macdonald functions and their group-theoretical sense
https://doi.org/10.22405/2226-8383-2021-22-1-225-233
Abstract
Two formulas for Macdonald functions (which are a widely known in mathematics and applications particular case of cylinder functions) are obtained by using some integral bilinear functionals defined on a pair of representation spaces or a square of these spaces
About the Authors
Alexander Ivanovich Nizhnikov
Moscow State Pedagogical University
Russian Federation
Russian Federation
Ilya Anatolyevich Shilin
National Research University MPEI; Moscow State Pedagogical
University
Russian Federation
Russian Federation
References
1. Vilenkin N. Ja. 1965, Special functions and group representations theory, Nauka, Moscow. (In Russian.)
2. Gelfand I. M., Graev M. I., Vilenkin N.Ya. 1962, Integral geometry and related aspects in group representation theory, Fizmatlit, Moscow. (In Russian.)
3. Gradstein I. S., Ryzhik I.M˙ . 1963, Tables of integrals, sums, series and products, Fizmatlit, Moscow. (In Russian.)
4. Prudnikov A. P., Brychkov Yu. A., Marichev O. I. 1986, Integrals and series: Advanced chapters, Nauka, Moscow. (In Russian.)
5. Prudnikov A. P., Brychkov Yu. A., Marichev O. I. 198s, Integrals and series: Special functions, Nauka, Moscow. (In Russian.)
6. Prudnikov A. P., Brychkov Yu. A., Marichev O. I. 1981, Integrals and series: Elementary functions, Nauka, Moscow. (In Russian.)
7. Shilin I. A. 2012, “Double S0(2, 1)-invariant integrald and formulas for Whittaker functions“, Izv. VUZ., no. 5, pp. 56-66.
8. Aurich R., Lustig S. & Steiner F. 2004, “Hyperbolic universes with a horned topology and the cosmic microwave background anisotropy“, Classical and Quantum Gravity, vol. 21, pp.
9. -4925.
10. Bolte J., Steil G. & Steiner F. 1992, “Arithmetical chaos and violation of universality in energy level statistics“, Physical Review Letters, vol. 69, pp. 2188-2191.
11. Booker A. R. 2000, “A test for identifying Fourier coefficients of automorphic forms and applications to Kloosterman sums“, Experimental Mathematics, vol. 9, pp. 571-581.
12. Bryson A. E. 1994, Control of spacecraft and aircraft, Princeton University Press, Princeton.
13. Heijhal D. A. 1983, The Selberg trace formula for PSL(2,R). Lecture Notes in Mathematics, Volume 1001, Springer, Berlin.
14. Heijhal D. A. & Rackner B. N. 1992, “On the topography of Maass vaveforms for PSL(2,Z)“, Experimental Math., vol. 1, pp. 275-305.
15. Gil A., Seguna J. & Temme N. M. 2003, “Computation of the modified Bessel functions of the third kind of imaginary orders: uniform Airy-type asymptotic expansions“, J. Comp. Appl.
16. Math., vol. 153, pp. 225-234.
17. Iwaniec H. 1995, Introduction to the spectral theory of automorphic forms, Revista Matematica Iberoamericana, Madrid.
Review
For citations:
Nizhnikov A.I., Shilin I.A. On two formulas for Macdonald functions and their group-theoretical sense. Chebyshevskii Sbornik. 2021;22(1):225-233. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-1-225-233
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