Abstract
In this chapter the range of an analytic function is investigated. A generic problem of this type is the following: Let ℱ be a family of analytic functions on a region G which satisfy some property P. What can be said about f(G) for each f in ℱ? Are the sets f(G) uniformly big in some sense? Does there exist a ball B(a; r) such that f(G) ⊃ B(a; r) for each f in ℱ? Needless to say. the answers to such questions depend on the property P that is used to define ℱ.
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© 1978 Springer Science+Business Media, Inc.
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Conway, J.B. (1978). The Range of an Analytic Function. In: Functions of One Complex Variable I. Graduate Texts in Mathematics, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6313-5_12
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DOI: https://doi.org/10.1007/978-1-4612-6313-5_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94234-6
Online ISBN: 978-1-4612-6313-5
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