Tight Multiwavelet Frames with Different Matrix Dilations and Matrix Translations

REFERENCES

• M. Bownik ( 2000 ). A characterization of affine dual frames in L 2(R n ) . Appl. Comput. Harmonic Anal. 8 ( 2 ): 203 – 221 .
   Google Scholar
• A. Calogero ( 1999 ). Wavelets on general lattices associated with general expanding maps of R n . ERA Amer. Math. Soc. 5 ( 1 ): 1 – 10 .
   Google Scholar
• A. Calogero ( 2000 ). A Characterization of wavelets on general lattices . J. Geom. Anal. 10 ( 4 ): 597 – 622 .
   Google Scholar
• C.K. Chui , W. Czaja , M. Maggioni , and G. Weiss ( 2002 ). Characterization of general tight wavelet frames with matrix dilations and tightness preserving oversampling . J. Fourier Anal. Appl. 8 ( 2 ): 174 – 200 .
   Google Scholar
• C.K. Chui and X.L. Shi ( 2000 ). Orthonormal wavelets and tight frames with arbitrary real dilation . Appl. Comput. Harmonic Anal. 9 ( 2 ): 243 – 264 .
   Google Scholar
• S.S. Goh , A. Ron , and Z.W. Shen ( eds.) (2007 ). Gabor and Wavelet Frames . Singapore , World Scientific .
   Google Scholar
• E. Hernandez and G. Weiss (1996). A First Course on Wavelets . New York , CRC Press.
   Google Scholar
• B.B. Li , D.F. Li , and X.L. Shi ( 2009 ). Characterization of multiwavelet with different real dilations and translations . Acta Math. Hungar. 124 ( 1–2 ): 41 – 57 .
   Google Scholar
• D.F. Li and X.L. Shi ( 2009 ). A sufficient condition for affine frames with matrix dilations . Anal. Theory Appl. 25 ( 2 ): 166 – 174 .
   Google Scholar
• B. Liu and W.C. Sun ( 2009 ). Homogeneous approximation property for multivariate continuous wavelet transform . Numer. Func. Anal. Optim. 30 ( 7–8 ): 784 – 798 .
   Web of Science ®Google Scholar
• X.L. Shi and F. Chen ( 2005 ). Necessary conditions and sufficient conditions of affine frame . Science in China (Series A) 48 ( 12 ): 1369 – 1378 .
   Google Scholar
• X.L. Shi and Q.L. Shi ( 2005 ). A new criterion of affine frame . Chin. Ann. of Math. (Series A) 26 ( 2 ): 257 – 262 .
   Google Scholar
• E.M. Stein ( 1970 ). Singular Integrals and Differentiability Properties of Functions . Princeton , NJ , Princeton University Press .
   Google Scholar
• Z.J. Zhao and W.C. Sun ( 2008 ). Sufficient conditions for irregular wavelet frames . Numer. Functional Anal. Optim. 29 ( 11–12 ): 1394 – 1407 .
   Web of Science ®Google Scholar