IJPAM: Volume 52, No. 3 (2009)

A GENERALIZATION OF RIESZ POTENTIALS
AND FRACTIONAL POWERS OF
DIFFERENTIAL OPERATORS

Rubén Alejandro Cerutti
Facultad de Ciencias Exactas y Naturales y Agrimensura
Universidad Nacional del Nordeste
Avda. Libertad, 5540 (3400) Corrientes, ARGENTINA
e-mail: rcerutti@exa.unne.edu.ar


Abstract.In this short paper an operator obtained by convolution with a distributional function wich belongs to the $\{W_\alpha(P,m,n)\}_{\alpha\in\C}$ familie is presented. From it as particular cases one may obtain both, elliptic or hyperbolic Riesz potentials. Certain elementary properties are studied and the inversion problem is presented using, as principal tool, the Laplace transform.

Moreover we obtain an expression that may be interpreted as a fractional power of the ultrahyperbolic differential operator.

Received: March 17, 2009

AMS Subject Classification: 46F10

Key Words and Phrases: fractional power, hyperbolic differential operator, Riesz potential

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 3