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Mat. Tr., 2012, Volume 15, Number 1, Pages 141–154 (Mi mt232)  

Double exponential map on symmetric spaces

Yu. G. Nikonorov

Southern Mathematical Institute of the Vladikavkaz Scientific Center of RAS, Vladikavkaz, Russia

Abstract: We establish an asymptotic formula for the double exponential map operator on affine symmetric spaces. This operator plays an important role in the geometric calculus of symbols of (pseudo)differential operators on manifolds with connection, whose foundations were laid by Sharafutdinov. To obtain this result, we essentially use the structural theory of symmetric spaces and techniques of the Lie group theory. One of the key moments is an application of the Campbell–Hausdorff series in Dynkin form.

Key words: Riemannian manifold, (pseudo)differential operator on a manifold, homogeneous space, symmetric space, Lie group.

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English version:
Siberian Advances in Mathematics, 2013, 23:3, 210–218

Bibliographic databases:

Document Type: Article
UDC: 514.76+517.98+512.812
Received: 01.03.2011

Citation: Yu. G. Nikonorov, “Double exponential map on symmetric spaces”, Mat. Tr., 15:1 (2012), 141–154; Siberian Adv. Math., 23:3 (2013), 210–218

Citation in format AMSBIB
\Bibitem{Nik12}
\by Yu.~G.~Nikonorov
\paper Double exponential map on symmetric spaces
\jour Mat. Tr.
\yr 2012
\vol 15
\issue 1
\pages 141--154
\mathnet{http://mi.mathnet.ru/mt232}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2984681}
\elib{http://elibrary.ru/item.asp?id=17718103}
\transl
\jour Siberian Adv. Math.
\yr 2013
\vol 23
\issue 3
\pages 210--218
\crossref{https://doi.org/10.3103/S1055134413030061}


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