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Preprint
An inductive Julia-Caratheodory theorem for Pick functions in two variables
arXiv (Cornell University)
27 May 2016
Abstract
We study the asymptotic behavior of Pick functions, analytic functions which
take the upper half plane to itself. We show that if a two variable Pick
function $f$ has real residues to order $2N-1$ at infinity and the imaginary
part of the remainder between $f$ and this expansion is of order $2N+1,$ then
$f$ has real residues to order $2N$ and directional residues to order $2N+1.$
Furthermore, $f$ has real residues to order $2N+1$ if and only if the $2N+1$-th
derivative is given by a polynomial, thus obtaining a two variable analogue of
a higher order Julia-Carath\'eodory type theorem.
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Details
- Title
- An inductive Julia-Caratheodory theorem for Pick functions in two variables
- Creators
- J. E Pascoe
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021879755304721