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Search: MSC category 30E15 ( Asymptotic representations in the complex domain )

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1. CMB Online first

Gauthier, Paul M; Sharifi, Fatemeh
Luzin-type holomorphic approximation on closed subsets of open Riemann surfaces
It is known that if $E$ is a closed subset of an open Riemann surface $R$ and $f$ is a holomorphic function on a neighbourhood of $E,$ then it is ``usually" not possible to approximate $f$ uniformly by functions holomorphic on all of $R.$ We show, however, that for every open Riemann surface $R$ and every closed subset $E\subset R,$ there is closed subset $F\subset E,$ which approximates $E$ extremely well, such that every function holomorphic on $F$ can be approximated much better than uniformly by functions holomorphic on $R$.

Keywords:Carleman approximation, tangential approximation, Myrberg surface
Categories:30E15, 30F99

2. CMB 2001 (vol 44 pp. 420)

Gauthier, P. M.; Pouryayevali, M. R.
Approximation by Meromorphic Functions With Mittag-Leffler Type Constraints
Functions defined on closed sets are simultaneously approximated and interpolated by meromorphic functions with prescribed poles and zeros outside the set of approximation.

Categories:30D30, 30E10, 30E15

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