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Mat. Zametki, 1977, Volume 22, Issue 5, Pages 729–744 (Mi mz8095)  

This article is cited in 3 scientific papers (total in 3 papers)

Higher derivatives of mappings of locally convex spaces

O. G. Smolyanov

M. V. Lomonosov Moscow State University

Abstract: We establish sufficient conditions for $n$-fold bounded differentiability (“$b$-differentiability”) of mappings of locally convex spaces and sufficient conditions for $n$-fold Hyers-Lang differentiability (“$HL$-differentiability”) of mappings of pseudotopological linear spaces. We describe a class of locally convex spaces on which there exist everywhere infinitely $b$-differentiable real functions which are not everywhere continuous (and so are not everywhere $HL$-differentiable). Our results show, in particular, that for a wide class of locally convex spaces a significant number of the known definitions of $C^\infty$-mappings fall into two classes of equivalent definitions.

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English version:
Mathematical Notes, 1977, 22:5, 899–906

Bibliographic databases:

UDC: 513.8
Received: 18.05.1976

Citation: O. G. Smolyanov, “Higher derivatives of mappings of locally convex spaces”, Mat. Zametki, 22:5 (1977), 729–744; Math. Notes, 22:5 (1977), 899–906

Citation in format AMSBIB
\Bibitem{Smo77}
\by O.~G.~Smolyanov
\paper Higher derivatives of mappings of locally convex spaces
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 5
\pages 729--744
\mathnet{http://mi.mathnet.ru/mz8095}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=494216}
\zmath{https://zbmath.org/?q=an:0369.46038}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 5
\pages 899--906
\crossref{https://doi.org/10.1007/BF01098355}


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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. E. T. Shavgulidze, “On a diffeomorphism of a locally convex space”, Russian Math. Surveys, 34:5 (1979), 245–246  mathnet  crossref  mathscinet  zmath
    2. S. G. Lobanov, O. G. Smolyanov, “Ordinary differential equations in locally convex spaces”, Russian Math. Surveys, 49:3 (1994), 97–175  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Bogachev V. Smolyanov O., “Topological Vector Spaces and Their Applications”, Topological Vector Spaces and Their Applications, Springer Monographs in Mathematics, Springer, 2017, 1–456  crossref  isi
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