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On the convolution equation related to the diamond Klein-Gordon operator. (English) Zbl 1243.46033
Summary: We study the distribution e αx (+m 2 ) k δ for m0, where (+m 2 ) k is the diamond Klein-Gordon operator iterated k times, δ is the Dirac delta distribution, x=(x 1 ,x 2 ,,x n ) is a variable in n , and α=(α 1 ,α 2 ,,α n ) is a constant. In particular, we study the application of e αx (+m 2 ) k δ for solving the solution of some convolution equation. We find that the types of solution of such a convolution equation, such as an ordinary function or a singular distribution, depend on the relationship between k and M.
MSC:
46F12Integral transforms in distribution spaces