IJPAM: Volume 64, No. 3 (2010)

ON THE DISTRIBUTION $\left(m^2-P\pm i0\right)^\lambda$

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

Abstract.In this paper the well-known one dimensional distribution $\left(
1-t^{2}\right) _{+}^{\lambda }$ is generalized for the distribution $\left( m^{2}-P\pm i0\right)^\lambda$, where $P$ is a non degenerate quadratic form and $m$ is a real positive number.

Also we introduce the generalized functions $\left( m^{2}-P\right)
_{+}^{\lambda }$ and $\left( P-m^{2}\right) _{+}^{\lambda }$, and by using a method by Gelfand and Shilov, the Fourier transform of this new generalized function is obtained.

Received: June 17, 2010

AMS Subject Classification: 46F10

Key Words and Phrases: distribution theory, generalized functions connected with quadratic forms

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