Meromorphic Extendibility and Rigidity of Interpolation
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2010
- DOI:
- arXiv:
- arXiv:1011.5003
- Bibcode:
- 2010arXiv1011.5003R
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 30E25
- E-Print:
- J. Math. Anal. Appl. 377, 828--833, 2011