核竹中-马尔姆奎斯特系统与边界加权哈代空间中的自适应逼近
Kernel Takenaka-Malmquist Systems and Adaptive Approximation in Boundary Weighted Hardy Spaces
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中文总结 AI 辅助
研究在边界加权哈代空间设定下的核-TM系统及相关逼近理论，通过建立双零AFD等方法，发展了广义哈代空间中的稀疏表示，还回顾了相关再生核希尔伯特空间子类及核-TM系统可容许性。
中文摘要 AI 辅助
竹中-马尔姆奎斯特（TM）系统作为三角函数系统的推广，在单位开圆盘和上半复平面的逼近理论中起决定性作用。本文在边界加权哈代空间的设定下，发展了核-TM系统及相关逼近理论。除自适应傅里叶分解（AFD）外，还建立了双零AFD（DAFD）作为广义哈代空间中的一种先进稀疏表示。文中还简要回顾了几个常见的再生核希尔伯特空间作为经典哈代空间的子类，并特别关注核-TM系统的可容许性。
英文摘要
Takenaka-Malmquist (TM) systems, as generalizations of the trigonometric function system, play a decisive role in approximation theory on the open unit disc and the upper-half complex plane. In the present paper with the setting of boundary weighted Hardy spaces we develop what we call kernel-TM systems and related approximation theory aspects. In such framework, besides adaptive Fourier decomposition (AFD), we also establish double-zero AFD (DAFD)as an advanced sparse representation in the generalized Hardy spaces. The paper also includes brief reviews of several commonly studied RKHSs as subclasses of the classical Hardy space with particular attention to admissibility of kernel-TM systems.
