IJPAM: Volume 52, No. 3 (2009)
AND FRACTIONAL POWERS OF
Facultad de Ciencias Exactas y Naturales y Agrimensura
Universidad Nacional del Nordeste
Avda. Libertad, 5540 (3400) Corrientes, ARGENTINA
Abstract.In this short paper an operator obtained by convolution with a distributional function wich belongs to the 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