## Abstract and Applied Analysis

### On Analog of Fourier Transform in Interior of the Light Cone

Tatyana Shtepina

#### Abstract

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

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 685794, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606517

Digital Object Identifier
doi:10.1155/2014/685794

Mathematical Reviews number (MathSciNet)
MR3248872

Zentralblatt MATH identifier
07022877

#### Citation

Shtepina, Tatyana. On Analog of Fourier Transform in Interior of the Light Cone. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 685794, 7 pages. doi:10.1155/2014/685794. https://projecteuclid.org/euclid.aaa/1412606517

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