Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ZEROS OF NEW BERGMAN KERNELS

  • Ghiloufi, Noureddine (Department of mathematics College of Science King Faisal University, University of Gabes Faculty of Sciences of Gabes LR17ES11 Mathematics and Applications) ;
  • Snoun, Safa (University of Gabes Faculty of Sciences of Gabes LR17ES11 Mathematics and Applications)
  • Received : 2020.07.01
  • Accepted : 2021.04.12
  • Published : 2022.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we determine explicitly the kernels 𝕜α,β associated with new Bergman spaces A2α,β(𝔻) considered recently by the first author and M. Zaway. Then we study the distribution of the zeros of these kernels essentially when α ∈ ℕ where the zeros are given by the zeros of a real polynomial Qα,β. Some numerical results are given throughout the paper.

Keywords

References

  1. S. Bergman, The Kernel Function and Conformal Mapping, second, revised edition, Mathematical Surveys, No. V, American Mathematical Society, Providence, RI, 1970.
  2. J. P. Demailly, Complex analytic and differential geometry, e-book evaluable at https://www-fourier.ujf-grenoble.fr/~demailly/documents.html
  3. N. Ghiloufi and M. Zaway, Meromorphic Bergman spaces, accepted for publication in Ukrainian Mathematical Journal.
  4. H. Hedenmalm, B. Korenblum, and K. Zhu, Theory of Bergman Spaces, Graduate Texts in Mathematics, 199, Springer-Verlag, New York, 2000. https://doi.org/10.1007/978-1-4612-0497-8
  5. S. G. Krantz, Geometric Analysis of the Bergman Kernel and Metric, Graduate Texts in Mathematics, 268, Springer, New York, 2013. https://doi.org/10.1007/978-1-4614-7924-6
  6. K. Zhu, Translating inequalities between Hardy and Bergman spaces, Amer. Math. Monthly 111 (2004), no. 6, 520-525. https://doi.org/10.2307/4145071