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Original Articles

Homogeneous Approximation Property for Multivariate Continuous Wavelet Transforms

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Pages 784-798 | Published online: 30 Aug 2009

REFERENCES

  • R. Balan , P.G. Casazza , C. Heil , and Z. Landan ( 2006 ). Density, overcompleteness, and localization of frames, I. Theory . J. Fourier Anal. Appl. 12 : 105 – 143 .
  • O. Christensen ( 2003 ). An Introduction to Frames and Riesz Bases . Birkhäuser , Boston .
  • O. Christensen , B. Deng , and C. Heil ( 1999 ). Density of Gabor frames . Appl. Comput. Harmon. Anal. 7 : 292 – 304 .
  • C.K. Chui , W. He , and J. Stöckler ( 2002 ). Compactly supported tight and sibling frames with maximum vanishing moments . Appl. Comput. Harmon. Anal. 13 : 224 – 262 .
  • C.K. Chui and X.L. Shi ( 2000 ). Orthonormal wavelets and tight frames with arbitrary dilations . J. Fourier Anal. Appl. 9 : 243 – 264 .
  • I. Daubechies ( 1992 ). Ten Lectures on Wavelets . SIAM , Philadelphia .
  • R.G. Duffin and A.C. Schaeffer ( 1952 ). A class of nonharmonic Fourier series . Trans. AMS 72 : 341 – 366 .
  • H.G. Feichtinger , W. Sun , and X. Zhou ( 2007 ). Two Banach spaces of atoms for stable wavelet frame expansions . J. Approx. Theory 146 : 28 – 70 .
  • K. Gröchenig ( 2004 ). Localization of frames, Banach frames, and the invertibility of the frame operator . J. Fourier. Anal. Appl. 10 : 105 – 132 .
  • K. Gröchenig ( 2008 ). The homogeneous approximation property and the comparison theorem for coherent frames . Sampl. Theory Signal Image Proc. 7 : 271 – 279 .
  • K. Gröchenig and H. Razafinjatovo ( 1996 ). On Landau's necessary density conditions for sampling and interpolation of band-limited functions . J. London Math. Soc. 54 : 557 – 565 .
  • C. Heil ( 2007 ). History and evolution of the density theorem for Gabor frames . J. Fourier Anal. Appl. 13 : 113 – 166 .
  • C. Heil and G. Kutyniok ( 2003 ). Density of weighted wavelet frames . J. Geom. Anal. 13 : 479 – 493 .
  • C. Heil and G. Kutyniok ( 2007 ). The homogeneous approximation property for wavelet frames . J. Approx. Theory 147 : 28 – 46 .
  • M. Holschneider and Ph. Tchamitchain ( 1991 ). Pointwise analysis of Riemann's “nondifferentiable” function . Invent. Math. 105 : 157 – 175 .
  • C. Heil and D. Walnut ( 1989 ). Continuous and discrete wavelet transforms . SIAM Review 31 : 628 – 666 .
  • G. Kutyniok ( 2007 ). Affine Density in Wavelet Analysis . Lecture Notes in Mathematics 1914 , Springer-Verlag , Berlin .
  • B. Liu and W. Sun ( 2008 ). Homogeneous approximation property for continuous wavelet transforms . J. Approx. Theory 155 : 111 – 124 .
  • J. Ramanathan and T. Steger ( 1995 ). Incompleteness of sparse coherent states . Appl. Comput. Harmon. Anal. 2 : 148 – 153 .
  • A. Ron and Z. Shen ( 1997 ). Affine systems in L 2(ℝ d ): the analysis of the analysis operator . J. Funct. Anal. 148 : 408 – 447 .
  • W. Sun , Homogeneous approximation property for wavelet frames . Monatsh. Math. (to appear) doi: dx.doi.org110.1007/s00605-008-0055-1 .
  • W. Sun and X. Zhou ( 2000 ). Irregular wavelet frames . Science in China, Series A 43 : 122 – 127 .
  • W. Sun and X. Zhou ( 2002 ). Irregular wavelet/Gabor frames . Appl. Comput. Harmon. Anal. 13 : 63 – 76 .
  • W. Sun and X. Zhou ( 2003 ). Density and stability of wavelet frames . Appl. Comput. Harmon. Anal. 15 : 117 – 133 .

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