Injective matrix functions
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- by Binyamin Schwarz PDF
- Proc. Amer. Math. Soc. 83 (1981), 331-336 Request permission
Abstract:
Univalence of holomorphic (scalar) functions $f(z)$ is generalized to injectivity of holomorphic matrix functions $V(z) = ({\upsilon _{ik}}(z))_1^n$. Local injectivity is characterized by $\left | {V’({z_0})} \right | \ne 0\left ( {\left | A \right | = \det A} \right )$. The classes $S$ and $\Sigma$ are defined as in the scalar case. For each class a sufficient condition is proved and a necessary condition is conjectured.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 331-336
- MSC: Primary 30C55; Secondary 15A54, 30G30
- DOI: https://doi.org/10.1090/S0002-9939-1981-0624924-3
- MathSciNet review: 624924