2005/02/07 by Alexander Tumanov, A. Tumanov, Tumanov, A.
Engineering · Mathematics · #Robotic Mechanisms and Dynamics #math.CV #msc:30E25 #msc:32V25
paper · pdf · doi:10.48550/arxiv.math/0502139
arxiv created 2005/02/07 · arxiv updated 2009/12/01
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.