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

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

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
2. S. G. Lobanov, O. G. Smolyanov, “Ordinary differential equations in locally convex spaces”, Russian Math. Surveys, 49:3 (1994), 97–175
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
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