On the Diamond Bessel Klein Gordon operator related to linear differential equation

Volume 12, Issue 8, pp 552--561 http://dx.doi.org/10.22436/jnsa.012.08.06

Publication Date: March 31, 2019 Submission Date: February 19, 2017 Revision Date: February 27, 2019 Accteptance Date: March 05, 2019

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Authors

Wanchak Satsanit - Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, 50290, Thailand.

Abstract

In this paper, first, we study the Green function of the Diamond Klein Gordon Bessel operator iterated \(k\) times. We give a sense of Distribution theory considering the properties of the convolution of the Green function. Finally, we solve the following equation \[ \left(\diamondsuit_{B}+d^{2}\right)^k u(x)=\sum^{m}_{r=0}c_{r}\left(\diamondsuit_{B}+d^{2}\right)^{k}\delta.\] It was found that the type of above equation depend on the relationship between the value \(k\) and \(m\).

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Keywords

• Diamond Bessel operator
• Diamond Klein Gordon Bessel operator
• tempered distribution

MSC

•  46F10
•  46F12

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