IJPAM: Volume 66, No. 4 (2011)

A NEW FRACTIONAL FOURIER TRANSFORM AND
CONVOLUTION PRODUCTS

Luis Guillermo Romero$^1$, Rubén Alejandro Cerutti$^2$,
Luciano Leonardo Luque$^3$
$^{1,2,3}$Faculty of Exact Sciences
National University of Nordeste
Avda. Libertad 5540, Corrientes, 3400, ARGENTINA
$^2$e-mail: rcerutti@exa.unne.edu.ar


Abstract.In this short paper we introduce a new definition of the Fractional Fourier transform of order $\a$, , of a function wich belongs to the Lizorkin space of functions. The simplicity of their definition allows us to deal with a novel convolution product due by Miana [5] and with the Weyl fractional calculus. We also present an inversion formulae.

Received: September 10, 2010

AMS Subject Classification: 26A33, 42A38

Key Words and Phrases: fractional Fourier transform, convolution products, fractional operator

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