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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.

Abstract

We introduce an analog of Fourier transform in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of , namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that -transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.