The Reproducing Kernel Function for the Image Space of a Limited Spectrum Wavelet Transform

Abstract

In order to describe the nature of image space of the wavelet transform and a limited spectrum and decay faster wavelet，this paper uses Shannon scaling function to construct a wavelet function，take advantage of wavelet analysis theory to give the nature of image space of the wavelet transform and the wavelet transform. Fixing the scale factor，we get this wavelet transform as the space of two specific expressions of reproducing kernel function，take advantage of the reproducing kernel space theory to describe the wavelet transform of image space and provide the theoretical basis for numerical calculation of the wavelet.

Keywords

• reproducing kernel Hilbert space; wavelet function; wavelet transform; reproducing kernel function; scale factor