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On the Convolution Equation Related to the Diamond Klein‐Gordon Operator

Author

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  • Amphon Liangprom
  • Kamsing Nonlaopon

Abstract

We study the distribution eαx(⋄+m2) kδ for m ≥ 0, where (⋄+m2) k is the diamond Klein‐Gordon operator iterated k times, δ is the Dirac delta distribution, x = (x1, x2 … , xn) is a variable in ℝn, and α = (α1, α2, …, αn) is a constant. In particular, we study the application of eαx(⋄+m2) kδ for solving the solution of some convolution equation. We find that the types of solution of such convolution equation, such as the ordinary function and the singular distribution, depend on the relationship between k and M.

Suggested Citation

  • Amphon Liangprom & Kamsing Nonlaopon, 2011. "On the Convolution Equation Related to the Diamond Klein‐Gordon Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:908491
    DOI: 10.1155/2011/908491
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    References listed on IDEAS

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    1. Ram P. Kanwal, 1998. "Generalized Functions Theory and Technique," Springer Books, Springer, edition 0, number 978-1-4684-0035-9, October.
    2. Amphon Liangprom & Kamsing Nonlaopon, 2011. "On the Convolution Equation Related to the Diamond Klein-Gordon Operator," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, October.
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    Cited by:

    1. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).

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