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

This article is cited in 4 scientific papers (total in 4 papers)

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
Received: 12.07.1971

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  crossref  mathscinet  zmath
    2. Yu. A. Brychkov, “Asymptotic expansions of generalized functions. III”, Theoret. and Math. Phys., 23:2 (1975), 445–450  mathnet  crossref  mathscinet  zmath
    3. V. M. Shelkovich, “Associative and commutative distribution algebra with multipliers, and generalized solutions of nonlinear equations”, Math. Notes, 57:5 (1995), 536–549  mathnet  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математические заметки Mathematical Notes
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