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Reproducing kernels of some weighted Bergman spaces. (English) Zbl 1477.32005

Summary: Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.

MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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References:

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