A decomposition of functions with zero means on circles

Details A decomposition of functions with zero means on circles A decomposition of functions with zero means on circles

2003-11-14

arxiv.org/abs/math/0311236v1

Mathematics

Complex Variables

Scientific paper

It is well known that every Hoelder-continuous function on the unit circle is the sum of two functions such that one of these two functions extends holomorphically into the unit disc and the other extends holomorphically into the complement of the unit disc. In the paper we prove that an analogue of this holds for Hoelder-continuous functions on an annulus A which have zero averages on all circles contained in A which surround the hole.

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