Geodesic
On the Diamond Bessel Klein Gordon operator related to linear differential equation
Satsanit, Wanchak 1
1 Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, 50290, Thailand
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 8, p. 552-561.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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 $m$.
DOI : 10.22436/jnsa.012.08.06
Classification : 46F10, 46F12
Keywords: Diamond Bessel operator, Diamond Klein Gordon Bessel operator, tempered distribution

Satsanit, Wanchak  1

1 Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, 50290, Thailand 
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Satsanit, Wanchak . On the Diamond Bessel Klein Gordon  operator related to linear differential equation. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 8, p. 552-561. doi : 10.22436/jnsa.012.08.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.08.06/

[1] Bunpog, C.; Kananthai, A. On the Bessel Diamond operator, J. Appl. Functional Anal., Volume 2009 (2009), pp. 10-19

[2] Donoghue, W. F. Distributions and Fourier Transform, Academic Press, New York, 1969

[3] Kananthai, A. On the Solution of the n-Dimensional Diamond Operator, Appl. Math. Comput., Volume 88 (1997), pp. 27-37 | DOI

[4] Manuel, A.; Aguirre, T. Some properties of Bessel Elliptic kernel and Bessel ultra-hyperbolic kernel, Thai J. Math., Volume 6 (2008), pp. 171-190

[5] Nozaki, Y. On Riemann-Liouville integral of Ultra-hyperbolic type, Kōdai Math. Sem. Rep., Volume 16 (1964), pp. 69-87 | Zbl

[6] Trione, S. E. On Marcel Riesz's ultrahyperbolic kernel, Stud. Appl. Math., Volume 79 (1988), pp. 185-191 | Zbl | DOI

[7] Yildirim, H. Riesz potentials generated by a generalized shift operator, Ph.D. Thesis, Ankara University, Ankara, 1995

[8] Yildirim, H.; Sarikaya, M. Z.; Öztürk, S. The solution of the n-dimensional Bessel diamond operator and the Fourier-Bessel transform of their convolution, Proc. Indian Acad. Sci. Math. Sci., Volume 114 (2004), pp. 375-387 | DOI

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