Abstract
The definition is formulated of the asymptotic expansion of a generalized function depending on a parameter. A number of theorems are proved about the properties of asymptotic expansions and operations on them, in particular, theorems on differentiation and integration. For generalized functions of the formf (x)eixt,f (x) ɛS', t → ±∞ the relation is investigated between the singularity carrierf and the carrier of coefficient functionals.
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Translated from Matematicheskie Zametki, Vol. 12, No. 2, pp. 131–138, August, 1972.
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Brychkov, Y.A. Asymptotic expansions of generalized functions. Mathematical Notes of the Academy of Sciences of the USSR 12, 513–517 (1972). https://doi.org/10.1007/BF01095008
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DOI: https://doi.org/10.1007/BF01095008