Representations of analytic functions in terms of local values by means of the riemann mapping function

Abstract

For any analytic function f on a Riemann surface S, we give a “good” formula representing f on a large simplyconnected domain containing any given point pεS in terms of the values of f in any neighborhood at any fixed point p p _oεS, by using some Riemann mapping function.

Keywords:

• Representation of analytic function
• Representation of harmonic function
• Taylor expansion
• Analytic extension
• Convergence
• Riemann mapping function
• Confonnal mapping
• Inverse function
• Reproducing kernel

AMS Classifications:

• Primary:30B10
• 30C30
• 30C35