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

Amphon Liangprom and Kamsing Nonlaopon

Abstract and Applied Analysis, 2011, vol. 2011, 1-16

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 .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:908491

DOI: 10.1155/2011/908491

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