IJPAM: Volume 64, No. 3 (2010)

THE FOURIER TRANSFORM OF $((\sum_{i=1}^{n}a_{i}x_{i}^{2})^{m}\pm i0))^{\lambda }$

Manuel A. Aguirre
Núcleo Consolidado Matemática Pura y Aplicada (NuCoMPA)
Facultad de Ciencias Exactas
Universidad Nacional del Centro
Tandil, Provincia de Buenos Aires, ARGENTINA
e-mail: maguirre@exa.unicen.edu.ar

Abstract.Let $H$ be a quadratic form defined by ([*]). In this paper we give a sense to Fourier transform of $H^{\lambda }$ and $((%
\sum_{i=1}^{n}a_{i}x_{i}^{2})^{m}\pm i0)^{\lambda }$, where $\lambda $ is a complex number and $m=1,2,...$

As consequence we obtain the Fourier transform of the distributions family defined by ([*]).

Our results (cf. formulae ([*]) and ([*])) are a generalization of the Fourier transform of distributions $%
~(x_{1}^{2}+..+x_{p}^{2}-x_{p+1}^{2}-..-x_{p+q}^{2}\pm i0)^{\lambda }$, which appears in [#!G!#], p. 284.

Received: May 17, 2010

AMS Subject Classification: 43A32

Key Words and Phrases: quadratic forms, Fourier transform

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 3