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Mat. Tr., 2009, Volume 12, Number 1, Pages 3–25 (Mi mt173)  

This article is cited in 1 scientific paper (total in 1 paper)

On applications of the Taylor formula in some quasispaces

A. V. Greshnov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: We consider some metric spaces with quasimetric (quasispaces) comprising uniformly regular (equiregular) Carnot–Carathéodory quasispaces whose quasimetric is induced by $C^{\varUpsilon-1}$-smooth vector fields of formal degree not higher than $\varUpsilon$. For these spaces, some analogues of the Campbell–Hausdorff formula are derived, which allows us to prove a theorem on a nilpotent tangent cone, a theorem on isomorphism of various nilpotent tangent cones defined at a common point, and a local approximation theorem.

Key words: nilpotent group and algebra, canonical coordinates, vector field, the Taylor formula, the Campbell–Hausdorff–Dynkin formula, quasimetric, quasispace.

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English version:
Siberian Advances in Mathematics, 2010, 20:3, 164–179

Bibliographic databases:

UDC: 514.763+512.812.4+517.911
Received: 17.03.2008

Citation: A. V. Greshnov, “On applications of the Taylor formula in some quasispaces”, Mat. Tr., 12:1 (2009), 3–25; Siberian Adv. Math., 20:3 (2010), 164–179

Citation in format AMSBIB
\Bibitem{Gre09}
\by A.~V.~Greshnov
\paper On applications of the Taylor formula in some quasispaces
\jour Mat. Tr.
\yr 2009
\vol 12
\issue 1
\pages 3--25
\mathnet{http://mi.mathnet.ru/mt173}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2569646}
\elib{http://elibrary.ru/item.asp?id=12869659}
\transl
\jour Siberian Adv. Math.
\yr 2010
\vol 20
\issue 3
\pages 164--179
\crossref{https://doi.org/10.3103/S1055134410030028}
\elib{http://elibrary.ru/item.asp?id=15329445}


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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. A. V. Greshnov, “On the generalized triangle inequality for quasimetrics induced by noncommuting vector fields”, Siberian Adv. Math., 22:2 (2012), 95–114  mathnet  crossref  mathscinet
  • Математические труды Siberian Advances in Mathematics
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