Errata and supplements to: Orthonormal RBF Wavelet and Ridgelet-like Series and Transforms for High-Dimensional Problems

Abstract

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.