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On some completenesses
of the Bergman kernel and the Rudin kernel
Saburou Saitoh |
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Vol. 56 (1975), No. 2, 581–596
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Abstract |
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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)1∕2 < ∞. 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)1∕2 < ∞. The object of this paper is to discuss some problems of this type. |
Mathematical Subject Classification
Primary: 30A31
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Milestones
Received: 14 December 1973
Published: 1 February 1975
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Authors |
| Saburou Saitoh | |
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