On construction of periodic wavelet frames

A method for the construction of periodic dual wavelet frames is provided. The method is algorithmic, it allows to construct dual frames based on any suitable generating function. As a corollary, we describe a wide class of periodic functions which can be extended to a wavelet frame.

[1]  Zuowei Shen,et al.  Gramian Analysis of Affine Bases and Affine Frames. , 1995 .

[2]  A. Ron,et al.  Affine Systems inL2(Rd): The Analysis of the Analysis Operator , 1997 .

[3]  A. Ron,et al.  Affine systems inL2 (ℝd) II: Dual systems , 1997 .

[4]  Pavel Andrianov,et al.  On sufficient frame conditions for periodic wavelet systems , 2017, Int. J. Wavelets Multiresolution Inf. Process..

[5]  I. Daubechies,et al.  Framelets: MRA-based constructions of wavelet frames☆☆☆ , 2003 .

[6]  M. Skopina Local Convergence of Fourier Series with Respect to Periodized Wavelets , 1998 .

[7]  Maria Skopina,et al.  Wavelet Approximation of Periodic Functions , 2000 .

[8]  H. Mhaskar,et al.  On trigonometric wavelets , 1993 .

[9]  Say Song Goh,et al.  Construction of Schauder decomposition on banach spaces of periodic functions , 1998, Proceedings of the Edinburgh Mathematical Society.

[10]  C. Chui,et al.  A general framework of compactly supported splines and wavelets , 1992 .

[11]  Gilbert G. Walter,et al.  Periodic Wavelets from Scratch , 1999 .

[12]  A. Ron,et al.  Frames and Stable Bases for Shift-Invariant Subspaces of L2(ℝd) , 1995, Canadian Journal of Mathematics.

[13]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[14]  Nikolaos D. Atreas,et al.  Characterizations of dual multiwavelet frames of periodic functions , 2016, Int. J. Wavelets Multiresolution Inf. Process..

[15]  M. Skopina C A ] 1 8 A pr 2 00 7 Multivariate Wavelet Frames 1 , 2008 .

[16]  B. Han Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix , 2003 .

[17]  B. Han On Dual Wavelet Tight Frames , 1997 .

[18]  Say Song Goh,et al.  Tight periodic wavelet frames and approximation orders , 2011 .

[19]  E. Lebedeva On a connection between nonstationary and periodic wavelets , 2016, 1607.04898.