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Sbornik: Mathematics, 2012, Volume 203, Issue 3, Pages 307–325
DOI: https://doi.org/10.1070/SM2012v203n03ABEH004224 (Mi sm7812) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The spectral properties of distributions and asymptotic methods in perturbation theory

V. S. Belonosovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University
English version PDF (361 kB) Citations (6)
References:
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DOI: https://doi.org/10.1070/SM2012v203n03ABEH004224
Abstract: For differential equations of the form $x'=\varepsilon f(t,x;\varepsilon)$ in a Banach space a modification of the classical Krylov-Bogolyubov method is put forward. It allows complications in the construction of higher-order approximations which stem from the ‘small denominators problem’ to be avoided and many of the standard constraints on the behaviour of the function $f$ to be eliminated. The approach suggested is based on some results on the Fourier transforms of distributions.
Bibliography: 17 titles.
Keywords: method of averaging, spectrum, distributions, Fourier transform.
Received: 01.11.2010
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 3, Pages 3–22
DOI: https://doi.org/10.4213/sm7812
Bibliographic databases:
Document Type: Article
UDC: 517.928
MSC: Primary 34C29; Secondary 46F05
Language: English
Original paper language: Russian
Citation: V. S. Belonosov, “The spectral properties of distributions and asymptotic methods in perturbation theory”, Mat. Sb., 203:3 (2012), 3–22; Sb. Math., 203:3 (2012), 307–325
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v203/i3/p3
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:2130
    Russian version PDF:424
    English version PDF:15
    References:142
    First page:49
     
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