On the Fourier transform of the diamond Klein-Gordon kernel

International Journal of Pure and Applied Mathematics

Volumn 68, Issue 1, 2011, Pages 85-97

  Lunnaree, Apisit ^a   Nonlaopon, Kamsing ^a,b  

^a KHON KAEN UNIVERSITY   (Thailand)

^b Thailand Ministry of Science and Technology   (Thailand)

Author keywords

Diamond Klein Gordon kernel; Dirac delta distribution; Fourier transform; Tempered distribution

Indexed keywords

EID: 79953755104     PISSN: 13118080     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. I.M. Gel'fand, G.E. Shilov, Generalized Function. Vol. I: Properties and Operations, Academic Press, New York (1964).
2. A. Kananthai, On the convolution equation related to the diamond kernel of Marcel Riesz, Journal of Computational and Applied Mathematics, 100 (1998), 33-39. (Pubitemid 128383922)
3. A. Kananthai, On the convolution of the diamond kernel of Marcel Riesz, Appiled Mathematics and Computation, 114 (2000), 95-101.
4. A. Kananthai, On the diamond operator related to the wave equation, Nonlinear Analysis : Theory Methods Application, 47 (2001), 1373-138.
5. A. Kananthai, On the Fourier transfrom of the diamond kernel of Marcel Riesz, Appiled Mathematics and Computation, 101 (1999), 151-158. (Pubitemid 129590773)
6. A. Kananthai, On the nonlinear diamond operator related to the wave equation, Nonlinear Analysis: Real World Applications, 3 (2002), 465-470.
7. A. Kananthai, On the solution of the n-dimensional diamond operator, Appiled Mathematics and Computation, 88 (1997), 27-37.
8. K. Nonlaopon, A. Lunnaree, A. Kananthai, On the solutions of the n-dimensional diamond Klien-Gordon operator and their convolution, Mathematical Problems in Engineering, submitted.
9. Y. Nozaki, On Riemann-Liouville integral of ultra-hyperbolictype, Kodia Mathematical Seminar Report, 6 (1964), 69-87.
10. M.Z. Sarikaya, H. Yildirim, On the B-convolution of the Bessel diamond kernel of Riesz, Appiled Mathematics and Computation, 208 (2009), 18-22.
11. β (u,m), Mathematica note, 38 (1995-96), 105-111.
12. M.A. Tellez, A. Kananthai,On the convolution product of the distributional families related to the diamond operator, Le Matematiche, LVII (2002), 39-48.
13. S.E. Trione, On Marcel Riesz's ultra-hyperbolic kernel, Trabajos de Mathematica, 116 (1987), 1-12.
14. S.E. Trione, On the elementary retarded ultra-hyperbolic solution of the Klien-Gordon operator iterated k-times, Studies in Applied Mathematics, 79 (1988), 121-141.
15. λ ultrahyperbolic solution of the Klien-Gordon operator iterated k-times, Integral Transforms and Spacial Functions, 9 (2000), 149-162.
16. H. Yildirim, M.Z. Sarikaya, On the Bessel diamond and the nonlinear Bessel diamond operator related to the Bessel wave equation, Nonlinear Anal. Ser. A: Theory. Meth Appl, 68 (2008), 430-442. (Pubitemid 350016628)
17. H. Yildirim, M.Z. Sarikaya, S. Ozturk, The solution of n-diamensional Bessel diamond operator and the Fourier-Bessel transform of their convolution, Proc. Indian Acad. Sci.(Math. Sci), 114 (2004), 375-387.
18. A.H. Zemanian, Distribution Theory and Transform Analysis, McGraw-Hill, New York (1965).