The reproducing kernel Hilbert space based on wavelet transform

Abstract

In this paper, the explicit and analytic expression of the reproducing kernel function for the image space of the wavelet transform is obtained based on the fact that the image space of wavelet transform is a reproducing kernel Hilbert space. Here we describe in detail the reproducing kernel and structure of this space when the scale factor is fixed. This provides the theoretic basis for discussing the image space of general wavelet transform and broadens the scope of application of the reproducing kernel space theories.