On analytic injective matrix functions

Bshouty, D.; Hengartner, W.

doi:10.1090/S0002-9939-1983-0699414-4

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On analytic injective matrix functions
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by D. Bshouty and W. Hengartner PDF

Proc. Amer. Math. Soc. 88 (1983), 459-463 Request permission

Abstract:

An ingenious generalization of univalent functions of one complex variable into matrix functions was introduced by B. Schwarz, along with two conjectures corresponding to the first coefficient problem and the second coefficient problem for the traditional classes $\Sigma$ and $S$, respectively. We exhibit two counterexamples for these conjectures.

References

Binyamin Schwarz, Injective matrix functions, Proc. Amer. Math. Soc. 83 (1981), no. 2, 331–336. MR 624924, DOI 10.1090/S0002-9939-1981-0624924-3