[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2006.43.1.199

THE BERGMAN KERNEL FUNCTION AND THE SZEGO KERNEL FUNCTION

CHUNG YOUNG-BOK (Department of Mathematics Chonnam National University)

Publication Information

Journal of the Korean Mathematical Society / v.43, no.1, 2006 , pp. 199-213 More about this Journal

Abstract

We compute the holomorphic derivative of the harmonic measure associated to a $C^\infty$ bounded domain in the plane and show that the exact Bergman kernel function associated to a $C^\infty$ bounded domain in the plane relates the derivatives of the Ahlfors map and the Szego kernel in an explicit way. We find several formulas for the exact Bergman kernel and the Szego kernel and the harmonic measure. Finally we survey some other properties of the holomorphic derivative of the harmonic measure.

Keywords

Bergman kernel; Szego kernel; Ahlfors map; harmonic measure;

Citations & Related Records

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Reference

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