Testing analyticity on circles

Details Testing analyticity on circles Testing analyticity on circles

2005-02-07

arxiv.org/abs/math/0502139v1

Mathematics

Complex Variables

Scientific paper

Consider a continuous one parameter family of circles in complex plane that
contains two circles lying in the exterior of one another. Under mild
assumptions on the family, we prove that if a continuous function on the union
of the above circles extends holomorphically into each circle, then the
function is holomorphic in the interior of the union of the circles.

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