Characterization of polyanalytic functions by meromorphic extensions into chains of circles

Abstract

One-parameter smooth families of circles in the complex plane with the following property are described: a function is polyanalytic if and only if it has meromorphic extension inside any circle from the family, with the only singularity-a pole at the center.

References in corpus (2)

• Complex dimensions of real manifolds, attached analytic discs and parametric argument principle
• Analyticity of functions analytic on circles