Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 685794, 7 pages
http://dx.doi.org/10.1155/2014/685794
Research Article

On Analog of Fourier Transform in Interior of the Light Cone

Donetsk Institute of Municipal Economy, Bulavina Street 1, Donetsk 83053, Ukraine

Received 7 November 2013; Revised 6 May 2014; Accepted 7 May 2014; Published 6 August 2014

Academic Editor: Adem Kilicman

Copyright © 2014 Tatyana Shtepina. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean Spaces, Princeton University Press, 1971. View at MathSciNet
  2. N. Y. Vilenkin, Special Functions and Representations of Groups, Nauka, Moscow, Russia, 2nd edition, 1991. View at MathSciNet
  3. I. M. Gel'fand, M. I. Graev, and N. Y. Vilenkin, Integral Geometry and Representation Theory, Generalized Functions, vol. 5, Academic Press, New York, NY, USA, 1966.
  4. V. P. Burskii and T. V. Shtepina, “On the spectrum of an equivariant extension of the Laplace operator in a ball,” Ukrainian Mathematical Journal, vol. 52, no. 11, pp. 1679–1690, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  5. S. Helgason, Groups and Geometric Aanalysis, vol. 113, Academic Press, 1984. View at MathSciNet
  6. V. V. Shtepin and T. V. Shtepina, “An application of intertwining operators in functional analysis,” Izvestiya Mathematics, vol. 73, no. 6, pp. 1265–1288, 2009. View at Publisher · View at Google Scholar
  7. A. Erdélyi, “Die Funksche Integralgleichung der Kugelflächenfunktionen und ihre Übertragung auf die Überkugel,” Mathematische Annalen, vol. 115, no. 1, pp. 456–465, 1938. View at Publisher · View at Google Scholar · View at MathSciNet
  8. T. V. Shtepina, “A generalization of the Funk-Hecke theorem to the case of hyperbolic space,” Izvestiya: Mathematics, vol. 68, no. 5, pp. 1051–1061, 2004. View at Publisher · View at Google Scholar
  9. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series: Special Functions, vol. 2, Gordon & Breach, New York, NY, USA, 1990. View at MathSciNet
  10. T. V. Shtepina, “About representation as convolution of the operator, permutable with the operator quasiregular representations of group of Lorentz,” Trudy Instituta Prikladnoj Matematiki i Mekhaniki, vol. 7, pp. 225–228, 2002. View at Google Scholar