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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1972, Volume 12, Issue 2, Pages 131–138 (Mi mz9859)

Asymptotic expansions of generalized functions

Yu. A. Brychkov

Computer Center, Academy of Sciences of the USSR

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 form $f(x)e^{ixt}$, $f(x)\in S'$, $t\to\pm\infty$ the relation is investigated between the singularity carrier $f$ and the carrier of coefficient functionals.

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English version:
Mathematical Notes, 1972, 12:2, 513–517

Bibliographic databases:

UDC: 517.5

Citation: Yu. A. Brychkov, “Asymptotic expansions of generalized functions”, Mat. Zametki, 12:2 (1972), 131–138; Math. Notes, 12:2 (1972), 513–517

Citation in format AMSBIB
\Bibitem{Bry72} \by Yu.~A.~Brychkov \paper Asymptotic expansions of generalized functions \jour Mat. Zametki \yr 1972 \vol 12 \issue 2 \pages 131--138 \mathnet{http://mi.mathnet.ru/mz9859} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=318873} \zmath{https://zbmath.org/?q=an:0244.46050} \transl \jour Math. Notes \yr 1972 \vol 12 \issue 2 \pages 513--517 \crossref{https://doi.org/10.1007/BF01095008} 

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This publication is cited in the following articles:
1. Yu. A. Brychkov, “Asymptotic expansions of generalized functions. II”, Theoret. and Math. Phys., 15:3 (1973), 590–594
2. Yu. A. Brychkov, “Asymptotic expansions of generalized functions. III”, Theoret. and Math. Phys., 23:2 (1975), 445–450
3. V. M. Shelkovich, “Associative and commutative distribution algebra with multipliers, and generalized solutions of nonlinear equations”, Math. Notes, 57:5 (1995), 536–549
4. V. G. Danilov, V. P. Maslov, V. M. Shelkovich, “Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems”, Theoret. and Math. Phys., 114:1 (1998), 1–42
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