IJPAM: Volume 66, No. 4 (2011)

ON GENERALIZED FUNCTIONS CONNECTED
WITH THE FUNCTION P(2,x)

Rubén Alejandro Cerutti
Faculty of Exact Sciences
National University of Nordeste
Avda. Libertad 5540, Corrientes, 3400, ARGENTINA
e-mail: rcerutti@exa.unne.edu.ar


Abstract.A new family of generalized functions associated with the function $\P(2,x)=\left(\sum_{l=1}^{p}x_l^2\right)^2-\left(\sum_{l=p+1}^{p+q}x_l^2\right)^2$ is introduced. The functions of this family can be considered as a generalization of the distributions $(P\pm i0)^\lambda$ and others introduced by Gelfand and Shilov (cf. [1]), where $P$ is the non degenerate quadratic form $P=\sum_{l=1}^{p}x_l^2-\sum_{l=p+1}^{p+q}x_l^2$.

The Fourier transform is obtained and elementary properties are studied.

Received: March 8, 2010

AMS Subject Classification: 46F10, 16F12

Key Words and Phrases: distribution theory, generalized function, quadratic forms

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 4