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Representing Functions in H 2 on the Kepler Manifold via WPOAFD Based on the Rational Approximation of Holomorphic Functions

Author

Listed:
  • Zeyuan Song

    (School of Business, Shandong University, Weihai 264209, China
    School of Mathematics and Statistics, Shandong University, Weihai 264209, China)

  • Zuoren Sun

    (School of Business, Shandong University, Weihai 264209, China)

Abstract

The central problem of this study is to represent any holomorphic and square integrable function on the Kepler manifold in the series form based on Fourier analysis. Because these function spaces are reproducing kernel Hilbert spaces (RKHS), three different domains on the Kepler manifold are considered and the weak pre-orthogonal adaptive Fourier decomposition (POAFD) is proposed on the domains. First, the weak maximal selection principle is shown to select the coefficient of the series. Furthermore, we prove the convergence theorem to show the accuracy of our method. This study is the extension of work by Wu et al. on POAFD in Bergman space.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2729-:d:878494
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    References listed on IDEAS

    as
    1. Hoda Saky & Saeid Abbasbandy & Elyas Shivanian & Ding-Xuan Zhou, 2022. "Applying the Reproducing Kernel Method to Fractional Differential Equations with Periodic Conditions in Hilbert Space," Journal of Mathematics, Hindawi, vol. 2022, pages 1-10, May.
    2. Yaroslav Kholodov & Andrey Alekseenko & Viktor Kazorin & Alexander Kurzhanskiy, 2021. "Generalization Second Order Macroscopic Traffic Models via Relative Velocity of the Congestion Propagation," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    3. Qu, Wei & Qian, Tao & Li, Haichou & Zhu, Kehe, 2022. "Best kernel approximation in Bergman spaces," Applied Mathematics and Computation, Elsevier, vol. 416(C).
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