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A Variation of the Koebe Mapping in a Dense Subset of S

Published online by Cambridge University Press:  20 November 2018

D. Bshouty  and
W. Hengartner
D. Bshouty
Affiliation:
Technion, Haifa, Israel
W. Hengartner
Affiliation:
Université Laval, Québec, Québec
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Let H(U) be the linear space of holomorphic functions defined on the unit disk U endowed with the topology of normal (locally uniform) convergence. For a subset E ⊂ H(U) we denote by Ē the closure of E with respect to the above topology. The topological dual space of H(U) is denoted by H′(U).

Let D, 0 ∊ D, be a simply connected domain in C. The unique univalent conformal mapping ϕ from U onto D, normalized by ϕ(0) = 0 and ϕ′(0) > 0 will be called “the Riemann Mapping onto D”. Let S be the set of all normalized univalent functions

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 1 , 01 February 1987 , pp. 54 - 73
Copyright
Copyright © Canadian Mathematical Society 1987

References

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