IJPAM: Volume 55, No. 4 (2009)

ON THE GREEN FUNCTION OF THE OPERATOR
$\left(\otimes+m^6\right)^k$ RELATED TO THE DIAMOND OPERATOR

Wanchak Satsanit$^1$, Amnuay Kananthai$^2$
$^{1,2}$Department of Mathematics
Chiangmai University
Chiangmai, 50200, THAILAND
$^2$e-mail: malamnka@science.cmu.ac.th


Abstract.In this paper, we study the Green function of the operator $\left(\otimes+m^6\right)^k$ which is iterated $k-$times and $m$ is positive real number. At first we find the Green function of the operator $\left(\otimes+m^6\right)^k$ and after that we apply such a Green function to solve the solution of the equation $\left(\otimes+m^6\right)^kG(x)=f(x)$, where $f$ is a generalized function and $G(x)$ is an unknown for $x \in
\mathbb{R}^n.$

Received: August 8, 2009

AMS Subject Classification: 30Gxx, 34B27,

Key Words and Phrases: diamond operator, tempered distribution, generalized function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 4