IJPAM: Volume 28, No. 3 (2006)

ALMANSI FUNCTIONS IN ${\bf R}^n$

K.H. Abodayeh
Department of Mathematical Sciences
Prince Sultan University
P.O. Box 66833, Riyadh, 11586, KINGDOM OF SAUDI ARABIA
e-mail: kamal@oyp.psu.edu.sa


Abstract.Every polyharmonic function in a star domain has a representation given by Almansi [#!almansi!#]. Generalizing this representation, we introduce a class of functions called Almansi functions in an open set in ${\bf R}^n$, $n\geq 2$; and investigate their properties. In particular, every polyharmonic function in a star domain is an Almansi function.

Received: April 8, 2006

AMS Subject Classification: 31B30

Key Words and Phrases: polyharmonic functions, Almansi functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 28
Issue: 3