IJPAM: Volume 57, No. 1 (2009)

ON THE GREEN FUNCTION OF THE OPERATOR
$\left(\circledcirc+m^4\right)^k$ RELATED TO THE KLEIN-GORDON
OPERATOR AND HELMHOLTZ OPERATOR

Wanchak Satsanit
Department of Mathematics
Regina Coeli College
166, Charoenprathet Road Changkran, Chiang Mai, 50100, THAILAND
e-mail: [email protected]


Abstract.In this paper, we study the Green function of the operator $\left(\circledcirc+m^4\right)^k$ which is iterated $k-$times and $m$ is positive real number. At first we find the Green function of the operator $\left(\circledcirc+m^4\right)^k$ and after that we apply such a Green function to solve the solution of the equation $\left(\circledcirc+m^4\right)^kG(x)=f(x)$, where $f$ is a generalized function and $G(x)$ is an unknown for $x \in \mathbb{R}^n.$

Received: September 29, 2009

AMS Subject Classification: 34B27, 81Q05

Key Words and Phrases: Klein-Gordon operator, Helmholtz operator, tempered distribution, generalized function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 1