Journal article
A CONTROLLED TANGENTIAL JULIA-CARATHEODORY THEORY VIA AVERAGED JULIA QUOTIENTS
Analysis & PDE, v 14(6), pp 1773-1795
01 Jan 2021
Abstract
Let f : D -> Omega a complex analytic function. The Julia quotient is given by the ratio between the distance of f(z) to the boundary of Omega and the distance of z to the boundary of D. A classical Julia-Caratheodory-type theorem states that if there is a sequence tending to tau in the boundary of D along which the Julia quotient is bounded, then the function f can be extended to tau such that f is nontangentially continuous and differentiable at tau and f(tau) is in the boundary of Omega. We develop an extended theory when D and Omega are taken to be the upper half-plane which corresponds to averaged boundedness of the Julia quotient on sets of controlled tangential approach, so-called lambda-Stolz regions, and higher-order regularity, including but not limited to higher-order differentiability, which we measure using gamma-regularity. Applications are given, including perturbation theory and moment problems.
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Details
- Title
- A CONTROLLED TANGENTIAL JULIA-CARATHEODORY THEORY VIA AVERAGED JULIA QUOTIENTS
- Creators
- J. E. Pascoe - University of FloridaMeredith Sargent - University of Arkansas at FayettevilleRyan Tully-Doyle - University of New Haven
- Publication Details
- Analysis & PDE, v 14(6), pp 1773-1795
- Publisher
- Mathematical Science Publ
- Number of pages
- 23
- Grant note
- University of New Haven SRG Grant DMS 1606260 / National Science Foundation Mathematical Science Postdoctoral Research Fellowship; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000693610100005
- Scopus ID
- 2-s2.0-85115095644
- Other Identifier
- 991021879631204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied