On some completenesses of the Bergman kernel and the Rudin kernel

Type: Article

Publication Date: 1975-02-01

Citations: 23

DOI: https://doi.org/10.2140/pjm.1975.56.581

Abstract

ί Let L 2 (G) denote the Hubert space of analytic functions / which are regular in a region G and have finite norms: \ 1/2 \f(z)\ 2 dxdyj <°o. it is well-known that the set {K(z,Z\)\z\ E G} of the Bergman kernels for the class L 2 (G) is complete in L 2 (G).In this paper, for regular regions G in the plane, it is shown that the set {K(z, z,) | z x G G) is also complete in the Hubert space of analytic functions / which are regular in G and finite norms: ί \f(z)\ 2 ds) < oo.The object of this paper is to discuss some problems of this type.

Locations

  • Pacific Journal of Mathematics - View - PDF
  • Project Euclid (Cornell University) - View - PDF

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