Analyticity on families of circles
Josip Globevnik
Abstract
It is known that if f is a continuous function on the complex plane which extends holomorphically from each circle surrounding the origin then f is not necessarily holomorphic. In the paper we prove that if, in addition, f extends holomorphically from each circle belonging to an open family of circles which do not surround the origin then f is holomorphic.
Create a lesson
Related papers
Limit theorems for Coulomb gases on a Jordan curve in an external potential
Kurt Johansson, Thomas Wolfs
On Simply Connected Domains Supporting an Unbounded Analytic Function with Bounded Derivative
Cameron MacMahon
The Reciprocal Problem on Weighted Bergman Spaces
Guangfu Cao, Li He, Shuqing Zhang
On φ-Normality of Harmonic Mappings and Their Families
Gopal Datt, Ritesh Pal
Weak Asymptotic Symmetry of Quasisymmetric Embeddings on Quasilines
Katsuhiko Matsuzaki, Fei Tao
Target Geometry in Prescribed-Value Schwarz Lemmas for Harmonic Maps
Miljan Knežević, Miodrag Mateljević