The isometric identities and inversion formulas of complex continuous wavelet transforms

Abstract 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.

[1]  N. Aluru.  A point collocation method based on reproducing kernel approximations , 2000 .

[2]  Caixia Deng,et al.  Characterization of Image Space of a Wavelet Transform , 2006, Int. J. Wavelets Multiresolution Inf. Process..

[3]  S. Saitoh.  Quadratic inequalities deduced from the theory of reproducing kernels , 1987 .

[4]  Hui-Ping Wang,et al.  A Lagrangian reproducing kernel particle method for metal forming analysis , 1998 .

[5]  QU Yu-ling,et al.  EXPRESSING WAVELET TRANSFORM WITH REPRODUCING KERNEL , 2008 .

[6]  Deng Applied.  Characterization of Image Space of Gauss Wavelet Transform , 2008 .

[7]  Hiroshi Fujiwara,et al.  Fundamental Error Estimate Inequalities for the Tikhonov Regularization Using Reproducing Kernels , 2012 .

[8]  Saburou Saitoh,et al.  Inversion from different kinds of information and real inversion formulas of the Laplace transform from a finite number of data , 2010 .

[9]  S. Saitoh.  Representations of the norms in bergman-selberg spaces on strips and half planes * , 1992 .

[10]  I. Daubechies.  Ten Lectures on Wavelets , 1992 .

[11]  Mouattamid.  RECURSIVE REPRODUCING KERNELS HILBERT SPACES USING THE THEORY OF POWER KERNELS , 2012 .

[12]  Saburou Saitoh,et al.  Analyticity and smoothing effect for the Schrödinger equation , 1990 .

[13]  Narayana R Aluru,et al.  A reproducing kernel particle method for meshless analysis of microelectromechanical systems , 1999 .

[14]  Han Long,et al.  Construction and calculation of reproducing kernel determined by various linear differential operators , 2009, Appl. Math. Comput..

[15]  Luoqing Li,et al.  Wavelet-Hough Transform with Applications in Edge and Target Detections , 2006, Int. J. Wavelets Multiresolution Inf. Process..

[16]  Fazhan Geng,et al.  A novel method for solving a class of singularly perturbed boundary value problems based on reproducing kernel method , 2011, Appl. Math. Comput..

[17]  Boying Wu,et al.  Application of reproducing kernel method to third order three-point boundary value problems , 2010, Appl. Math. Comput..