Vol. 56, No. 2, 1975

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On some completenesses of the Bergman kernel and the Rudin kernel

Saburou Saitoh

Vol. 56 (1975), No. 2, 581–596
Abstract

Let L2(G) denote the Hilbert space of analytic functions f which are regular in a region G and have finite norms: ( G|f(z)|2dxdy)12 < . It is well-known that the set {K(z,z1)|zI G} of the Bergman kernels for the class L2(G) is complete in L2(G). In this paper, for regular regions Ġ in the plane, it is shown that the set {K(z,zI)|zI G} is also complete in the Hilbert space of analytic functions f which are regular in G and finite norms: ( ∂G|f(z)|2ds)12 < . The object of this paper is to discuss some problems of this type.

Mathematical Subject Classification
Primary: 30A31
Milestones
Received: 14 December 1973
Published: 1 February 1975
Authors
Saburou Saitoh