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Journal of Mathematical Sciences

, Volume 209, Issue 5, pp 665–682 | Cite as

Operator Lipschitz Functions in Several Variables and Möbius Transformations

  • A. B. Aleksandrov
Article
  • 33 Downloads

It is proved that if f is an operator Lipschitz function defined on n , then the function \( \frac{f\circ \varphi }{\left\Vert {\varphi}^{\prime}\right\Vert } \) is also operator Lipschitz for every Möbius transformation φ with f(φ(∞)) = 0. Hereφ′‖ denotes the operator norm of the Jacobian matrix φSimilar statements for operator Lipschitz functions defined on closed subsets of n are also obtained. Bibliography: 10 titles.

Keywords

Closed Subset Homogeneous Polynomial Orthogonal Transformation Linear Fractional Transformation Joint Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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