The isometric identities and inversion formulas of complex continuous wavelet transforms

摘要

The reproducing kernel function of the image space of a family of complex wavelet transforms is presented. An admissible wavelet is obtained by convolution computation. Next, the correlative characterisation of the image space of the family of complex wavelet transforms is provided when the scale is fixed. Furthermore, the isometric identities and inversion formulas are obtained, which provide a theoretic basis for investigating the image space of the general wavelet transform.