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

Amphon Liangprom | Zendy; Kamsing laopon | Zendy

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

Author(s) -

Amphon Liangprom,

Kamsing laopon

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/908491

Subject(s) - mathematics , iterated function , convolution (computer science) , operator (biology) , distribution (mathematics) , mathematical analysis , convolution power , dirac delta function , klein–gordon equation , variable (mathematics) , constant (computer programming) , pure mathematics , mathematical physics , fourier transform , quantum mechanics , physics , chemistry , computer science , fourier analysis , biochemistry , repressor , nonlinear system , machine learning , artificial neural network , transcription factor , fractional fourier transform , gene , programming language

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

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