Vol. 96, No. 2, 1981

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A characterization of the adjoint L-kernel of Szegő type

Saburou Saitoh

Vol. 96 (1981), No. 2, 489–493
Abstract

Let G be a bounded regular region in the complex plane and L(z,u) the adjoint L-kernel of Szegő kernel function K(z,ū) on G. Then, for any analytic function h(z) on G with a finite Dirichlet integral, it is shown that the equation

  ∫ ∫
1-      ′  2
π    G|h(z)|dx dy
∫   ∫                       2
=        |(h(z1)− h(z2))ˆL(z1,z2)| |dz1||dz2|
∂G  ∂G
holds. Furthermore, for any fixed nonconstant h(z), we show that the function L(z1,z2) on G × G is characterized by that equation in some class.

Mathematical Subject Classification 2000
Primary: 30C40
Secondary: 30F99
Milestones
Received: 3 November 1980
Published: 1 October 1981
Authors
Saburou Saitoh