Meromorphic Extendibility and Rigidity of Interpolation
Abstract
Let T be the unit circle, f be an α-Holder continuous function on T, α>1/2, and A be the algebra of continuous function in the closed unit disk 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∈ A such that f+h ≠ 0 on T.
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