On some solutions to the Klein-Gordon equation related to an integral of Sonine

Author:
Stuart Nelson

Journal:
Trans. Amer. Math. Soc. **154** (1971), 227-237

MSC:
Primary 35C15; Secondary 35Q99

DOI:
https://doi.org/10.1090/S0002-9947-1971-0415049-9

MathSciNet review:
0415049

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Abstract: An integral due to Sonine is used to obtain an expansion for special solutions of the Klein-Gordon equation. This expansion is used to estimate the norms as . These estimates yield results on the time decay of a fairly wide class of solutions to the Klein-Gordon equation.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1971-0415049-9

Keywords:
Klein-Gordon equation,
Cauchy problem,
asymptotic behavior,
estimate of norms,
Fourier transform,
Sonine's discontinuous integral,
Bessel functions

Article copyright:
© Copyright 1971
American Mathematical Society