色导数、色展开及相关空间
Chromatic Derivatives, Chromatic Expansions and Associated Spaces
摘要：
本文介绍了色导数和色展开的基本性质，并提供了一个适当的动机，引入这些概念。色导数是一种特殊的、数值鲁棒的线性微分算子，它对应于某些正交多项式族。色展开式是相应的特殊函数的级数，它同时具有Taylor展开式和Shannon展开式的最佳性质。这使得色导数和色扩展适用于涉及经验采样数据的领域，例如数字信号和图像处理。本文的第一部分是一个2页的扩展摘要。
英文摘要：
This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential operators which correspond to certain families of orthogonal polynomials. Chromatic expansions are series of the corresponding special functions, which possess the best features of both the Taylor and the Shannon expansions. This makes chromatic derivatives and chromatic expansions applicable in fields involving empirically sampled data, such as digital signal and image processing. The first section of this paper is a 2 page extended abstract.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
