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Mat. Sb., 2003, Volume 194, Number 1, Pages 103–120 (Mi msb708)  

This article is cited in 6 scientific papers (total in 7 papers)

Almost normed spaces of functions with polynomial asymptotic behaviour

L. D. Kudryavtsev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider a linear space of functions asymptotically approaching polynomials of degree not higher than a fixed one as the independent variable approaches infinity. Such a space cannot be normed if the functions in it possess a certain smoothness. For this reason the concept of almost normed space is introduced and the spaces in question, namely, spaces of functions asymptotically or strongly asymptotically approaching polynomials, are shown to be almost normed. The completeness of these spaces in the metric generated by their almost norm is also proved, the connection between the asymptotic approach and the strong asymptotic approach of functions to polynomials is studied, and a new (and shorter) proof of the criterion for the asymptotic approach of functions to polynomials is presented.

DOI: https://doi.org/10.4213/sm708

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English version:
Sbornik: Mathematics, 2003, 194:1, 105–122

Bibliographic databases:

Document Type: Article
UDC: 517.911
MSC: 46E10, 46E40
Received: 17.04.2002

Citation: L. D. Kudryavtsev, “Almost normed spaces of functions with polynomial asymptotic behaviour”, Mat. Sb., 194:1 (2003), 103–120; Sb. Math., 194:1 (2003), 105–122

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v194/i1/p103

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. D. Kudryavtsev, “Operators for almost normed spaces”, Dokl. Math., 71:2 (2005), 228–230  mathnet  mathscinet  zmath  zmath  isi  elib  elib
    2. L. D. Kudryavtsev, “Almost Normed and Quasinormed Spaces”, Proc. Steklov Inst. Math., 248 (2005), 125–137  mathnet  mathscinet  zmath
    3. A. A. Bolibrukh, V. A. Il'in, S. M. Nikol'skii, V. M. Filippov, G. N. Yakovlev, “Lev Dmitrievich Kudryavtsev (on his 80th birthday)”, Russian Math. Surveys, 60:1 (2005), 177–188  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. L. D. Kudryavtsev, “Lagrangian asymptotic behaviour of solutions of inhomogeneous systems of ordinary differential equations”, Sb. Math., 197:9 (2006), 1341–1351  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. L. D. Kudryavtsev, “Problems with asymptotic initial data for systems of ordinary differential equations”, Dokl. Math., 73:2 (2006), 202  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. Granata A., “Polynomial asymptotic expansions in the real domain: the geometric, the factorizational, and the stabilization approaches”, Anal. Math., 33:3 (2007), 161–198  crossref  mathscinet  zmath  elib
    7. S. A. Belyaev, “Solutions of ordinary differential equations asymptotically approaching polynomials in the reciprocal of an independent variable”, Dokl. Math., 80:1 (2009), 581  mathnet  crossref  mathscinet  zmath  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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