# Operator Lipschitz Functions in Several Variables and Möbius Transformations

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*It is proved that if f is an operator Lipschitz function defined on* ℝ^{ 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*. Here* ‖*φ*′‖ *denotes the operator norm of the Jacobian matrix φ*′ *Similar statements for operator Lipschitz functions defined on closed subsets of* ℝ^{ n } *are also obtained. Bibliography:* 10 *titles.*

## Keywords

Closed Subset Homogeneous Polynomial Orthogonal Transformation Linear Fractional Transformation Joint Spectrum
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## References

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