Meromorphic Extendibility and Rigidity of Interpolation

Details Meromorphic Extendibility and Rigidity of Interpolation Meromorphic Extendibility and Rigidity of Interpolation

2010-11-23

arxiv.org/abs/1011.5003v1

J. Math. Anal. Appl. 377, 828--833, 2011

Mathematics

Classical Analysis and ODEs

Scientific paper

Let T be the unit circle, f be an \alpha-Holder continuous function on T,
\alpha>1/2, and A be the algebra of continuous function in the closed unit disk
\bar D that are holomorphic in D. Then f extends to a meromorphic function in D
with at most m poles if and only if the winding number of f+h on T is bigger or
equal to -m for any h\in A such that f+h \neq 0 on T.

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