Zeros of new Bergman kernels
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In this paper we determine explicitly the kernels $\mathbb K_{\alpha,\beta}$ associated with new Bergman spaces $\mathcal A_{\alpha,\beta}^2(\mathbb D)$ considered recently by the first author and M. Zaway. Then we study the distribution of the zeros of these kernels essentially when $\alpha\in\mathbb N$ where the zeros are given by the zeros of a real polynomial $Q_{\alpha,\beta}$. Some numerical results are given throughout the paper.
Abstract
In this paper we determine explicitly the kernels $\mathbb K_{\alpha,\beta}$ associated with new Bergman spaces $\mathcal A_{\alpha,\beta}^2(\mathbb D)$ considered recently by the first author and M. Zaway. Then we study the distribution of the zeros of these kernels essentially when $\alpha\in\mathbb N$ where the zeros are given by the zeros of a real polynomial $Q_{\alpha,\beta}$. Some numerical results are given throughout the paper.
참고문헌 (6)
- S. Bergman, "The Kernel Function and Conformal Mapping" (1970), American Mathematical Society
- "Complex analytic and differential geometry, e-book evaluable"[URL]
- N. Ghiloufi, "Meromorphic Bergman spaces", Ukrainian Mathematical Journal
- H. Hedenmalm, "Theory of Bergman Spaces" (2000), Springer-Verlag
- S. G. Krantz, "Geometric Analysis of the Bergman Kernel and Metric" (2013), Springer
- K. Zhu, "Translating inequalities between Hardy and Bergman spaces", Amer. Math. Monthly, 111(6), pp.520~525 (2004)[DOI]