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Best kernel approximation in Bergman spaces

Author

Listed:
  • Qu, Wei
  • Qian, Tao
  • Li, Haichou
  • Zhu, Kehe

Abstract

Let H be a reproducing kernel Hilbert space of analytic functions on the unit disk D. The best kernel approximation problem for H is the following: given any positive integer n and any function f∈H find the best norm approximation of f by a linear combination of no more than n kernel functions K(z,zk), 1≤k≤n. The purpose of this paper is to prove the existence of best kernel approximation for weighted Bergman spaces with standard weights.

Suggested Citation

  • Qu, Wei & Qian, Tao & Li, Haichou & Zhu, Kehe, 2022. "Best kernel approximation in Bergman spaces," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    • Handle: RePEc:eee:apmaco:v:416:y:2022:i:c:s0096300321008316
    DOI: 10.1016/j.amc.2021.126749
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    Cited by:

    1. Lin, Cuiyun & Qian, Tao, 2024. "Frequency analysis with multiple kernels and complete dictionary," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. Zeyuan Song & Zuoren Sun, 2022. "Representing Functions in H 2 on the Kepler Manifold via WPOAFD Based on the Rational Approximation of Holomorphic Functions," Mathematics, MDPI, vol. 10(15), pages 1-15, August.

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