On the problem of multidimensional tauberian theory
Yu. N. Drozhzhinov
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
For generalized functions with Laplace transform has nonnegative imaginary part in tube domain over positive actant, we found sufficient conditions for existence of quasiasymptotic, the function with regular behavior with respect to which the quasiasymptotic exists being explicitly found. The obtained results are used to steady of the asymptotic behaviour of solutions of the Cauchy problem of passive operators.
Accepted: January 16, 2020
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