IJPAM: Volume 109, No. 3 (2016)

THE FOURIER TRANSFORM OF $\left( G(x,m)_{+}^{\lambda }\right)$

Manuel A. Aguirre$^1$, Emilio Aguirre Rébora$^2$
$^{1,2}$Núcleo Consolidado de
Matemática Pura y Aplicada
Facultad de Ciencias Exactas
Universidad Nacional del Centro
Buenos Aires, ARGENTINA

Abstract. In this article we give a sense the Fourier transform of

\begin{displaymath}\left( G(x,m)_{+}^{\lambda }\right) =\left( \left( \dsum\li... ...mits_{i=p+1}^{p+q}x_{i}^{2}\right) ^{m}\right) _{+}^{\lambda }.\end{displaymath}

In particular if $m=1$ we obtain the Fourier transform $\left( P(x)\right) _{+}^{\lambda }=\left( x_{1}^{2}+...+x_{p}^{2}-x_{p+1}^{2}-...-x_{p+q}^{2})\right) _{+}^{\lambda }$, where $p+q=n$ is the dimension of the space.

Received: May 31, 2016

Revised: July 21, 2016

Published: October 1, 2016

AMS Subject Classification: 46F10, 43A32

Key Words and Phrases: distributions, Fourier transform, ultrahyperbolic kernel
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DOI: 10.12732/ijpam.v109i3.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 3
Pages: 601 - 608


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