IJPAM: Volume 64, No. 3 (2010)

THE FOURIER TRANSFORM OF
$\delta ^{(k-1)}(M(x_{1}...x_{n}))$ AND $\delta ^{(k-1)}(c^{2}+M(x_{1}...x_{n}))$

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 $M(x_{1}...x_{n})$ and $V(x_{1}...x_{n})$ be the quadratic forms defined by (3) and (4), respectively. In this paper we obtain the Fourier transform of $ \delta ^{(k-1)}(V(x_{1}...x_{n})),\delta ^{(k-1)}(M(x_{1}...x_{n})), $ and $\delta ^{(k-1)}(c^{2}+M(x_{1}...x_{n}))$ and the expansion in series Taylor types of $ \delta ^{(k-1)}(c^{2}+M(x_{1}...x_{n})). $ Our formulae are generalization of the results that appear in [#!A1!#], p. 126 and [#!A4!#].

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