REPRESENTATION OF HOLOMORPHIC FUNCTIONS BY BOUNDARY INTEGRALS

@inproceedings{Baernstein1971REPRESENTATIONOH,
  title={REPRESENTATION OF HOLOMORPHIC FUNCTIONS BY BOUNDARY INTEGRALS},
  author={Albert Baernstein},
  year={1971}
}
Let K be a compact locally connected set in the plane and let /be a function holomorphic in the extended complement of K with/(oo) = 0. We prove that there exists a sequence of measures {p.n} on K satisfying lim"_" ||ju."||1'" = 0 such that f(z) = 2n=o iK (w—z)-"-1 du"(w) (z e K). It follows from the proof that two topologies for the space of functions holomorphic on K are the same. One of these is the inductive limit topology introduced by Kothe, and the other is defined by a family of… CONTINUE READING