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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

$ \Phi $-like holomorphic functions in $ {\bf C}\sp{n}$ and Banach spaces


Author: Kenneth R. Gurganus
Journal: Trans. Amer. Math. Soc. 205 (1975), 389-406
MSC: Primary 32A99; Secondary 30A32, 46G20
DOI: https://doi.org/10.1090/S0002-9947-1975-0374470-1
MathSciNet review: 0374470
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Abstract: In a recent paper, L. Brickman introduced the concept of $ \Phi $-like holomorphic functions as a complete generalization of starlike and spirallike functions of a single complex variable. In the present paper, the author extends this work to locally biholomorphic mappings of several complex variables and then to locally biholomorphic mappings defined in an arbitrary Banach space. Complete characterizations of univalency and starlikeness of locally biholomorphic maps in general Banach spaces are obtained.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0374470-1
Keywords: Univalent, starlike, spiral-like, $ \Phi $-like, Banach space, semi-inner product, holomorphic function
Article copyright: © Copyright 1975 American Mathematical Society