Representing Functions in H2 on the Kepler Manifold via WPOAFD Based on the Rational Approximation of Holomorphic Functions

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.