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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 𠑒 𠛼 𠑥 ( ⋄ + 𠑚 2 ) 𠑘 𠛿 for 𠑚 ≥ 0 , where ( ⋄ + 𠑚 2 ) 𠑘 is the diamond Klein-Gordon operator iterated 𠑘 times, 𠛿 is the Dirac delta distribution, 𠑥 = ( 𠑥 1 , 𠑥 2 , … , 𠑥 𠑛 ) is a variable in ℠𠑛 , and 𠛼 = ( 𠛼 1 , 𠛼 2 , … , 𠛼 𠑛 ) is a constant. In particular, we study the application of 𠑒 𠛼 𠑥 ( ⋄ + 𠑚 2 ) 𠑘 𠛿 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 𠑘 and 𠑀 .

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:908491
    DOI: 10.1155/2011/908491
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    Cited by:

    1. Kamsing Nonlaopon, 2019. "On the Inverse Ultrahyperbolic Klein-Gordon Kernel," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    2. Chalermpon Bunpog, 2018. "Boundary Value Problem of the Operator ⊕ k Related to the Biharmonic Operator and the Diamond Operator," Mathematics, MDPI, vol. 6(7), pages 1-11, July.

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