勘误与补充：用于高维问题的正交径向基函数小波与类脊波级数及变换
Errata and supplements to: Orthonormal RBF Wavelet and Ridgelet-like Series and Transforms for High-Dimensional Problems
AI总结：
本文纠正了作者先前关于正交RBF小波级数与变换论文中的勘误，并补充了最新进展，该方法利用微分算子解构造正交小波，避免张量积以处理高维问题。
摘要：
近年来，已有一些尝试将径向基函数（RBF）与小波联系起来，以处理高维多尺度问题。然而，据作者所知，文献中仍缺少正交和双正交的RBF小波。通过使用微分算子的非奇异通解和奇异基本解，作者近期在参考文献3中取得了实质性进展，推导出正交RBF小波级数和变换。该方法可推广至通过各类积分算子的正交卷积核函数来构造RBF小波。特别强调的是，所提出的RBF小波完全不使用张量积来处理多变量问题。本注释旨在纠正参考文献3中的一些勘误，并补充正交RBF小波变换研究中的若干最新进展。
英文摘要：
In recent years some attempts have been done to relate the RBF with wavelets in handling high dimensional multiscale problems. To the author's knowledge, however, the orthonormal and bi-orthogonal RBF wavelets are still missing in the literature. By using the nonsingular general solution and singular fundamental solution of differential operator, recently the present author, refer. 3, made some substantial headway to derive the orthonormal RBF wavelets series and transforms. The methodology can be generalized to create the RBF wavelets by means of the orthogonal convolution kernel function of various integral operators. In particular, it is stressed that the presented RBF wavelets does not apply the tensor product to handle multivariate problems at all. This note is to correct some errata in reference 3 and also to supply a few latest advances in the study of orthornormal RBF wavelet transforms.
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。
