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Siberian Advances in Mathematics

, Volume 23, Issue 3, pp 210–218 | Cite as

Double exponential map on symmetric spaces

  • Yu. G. Nikonorov
Article
  • 47 Downloads

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.

Keywords

Riemannian manifold (pseudo)differential operator on a manifold homogeneous space symmetric space Lie group 

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Copyright information

© Allerton Press, Inc. 2013

Authors and Affiliations

  1. 1.Southern Mathematical Institute of the Vladikavkaz Scientific Center of RASVladikavkazRussia

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