IJPAM: Volume 83, No. 2 (2013)

ON THE CONVOLUTION AND INVERSION OF
DIAMOND KLEIN GORDON KERNEL

Supaknaree Sattaso$^1$, Kamsing Nonlaopon$^2$
Department of Mathematics
Khon Kaen University
Khon Kaen 40002, THAILAND


Abstract. In this paper, we define the diamond Klein-Gordon Kernel $T_{\alpha}$ and the diamond Klein-Gordon operator of order $\alpha$ on the function $f$ by

\begin{displaymath} D^{\alpha}(f) =T_{\alpha}\ast f, \end{displaymath}

where $\alpha \in\mathbb{C}$, the symbol $\ast$ designates the convolution, and $f \in\mathcal{S},$ $\mathcal{S}$ is the Schwartz space of functions. In this paper, we aim to study the convolution of $T_{\alpha}$ and obtain the operator $L^{\alpha}=\left[D^{\alpha}\right]^{-1}$ such that if $D^{\alpha}(f)=\varphi$, then $L^{\alpha}\varphi=f.$

Received: November 8, 2012

AMS Subject Classification: 46F10, 46F12

Key Words and Phrases: diamond Klein-Gordon operator, diamond Klein-Gordon kernel, diamond operator, diamond kernel of Marcel Riesz, Dirac delta distribution

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DOI: 10.12732/ijpam.v83i2.12 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 2