Reproducing kernels for holomorphic functions on some balls related to the Lie ball

Volume 91 / 2007

Keiko Fujita Annales Polonici Mathematici 91 (2007), 219-234 MSC: 32A25, 30E20, 31B10. DOI: 10.4064/ap91-2-9

Abstract

We consider holomorphic functions and complex harmonic functions on some balls, including the complex Euclidean ball, the Lie ball and the dual Lie ball. After reviewing some results on Bergman kernels and harmonic Bergman kernels for these balls, we consider harmonic continuation of complex harmonic functions on these balls by using harmonic Bergman kernels. We also study Szegő kernels and harmonic Szegő kernels for these balls.

Authors

  • Keiko FujitaFaculty of Culture and Education
    Saga University
    Saga, 840-8502, Japan
    e-mail

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