Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 10
64
Views
2
CrossRef citations to date
0
Altmetric
Articles

Vector-stability of refinable vectors

&
Pages 2215-2228 | Received 15 Jun 2011, Accepted 22 Aug 2012, Published online: 28 Sep 2012

References

  • Cohen , A , Daubechies , I and Plonka , G . 1997 . Regularity of refinable function vectors . J. Fourier Anal. Appl. , 3 : 295 – 324 .
  • Heil , C and Colella , D . 1996 . Matrix refinement equations: Existence and uniqueness . J. Fourier Anal. Appl. , 2 : 363 – 378 .
  • Long , R , Chen , W and Yuan , S . 1997 . Wavelets generated by vector multiresolution analysis . Appl. Comput. Harmon. Anal. , 4 : 317 – 350 .
  • Jia , RQ and Micchelli , CA . 1991 . “ Using the refinement equations for the construction of pre-wavelets II: Powers of two ” . In Curves and Surfaces , Edited by: Laurent , P-J , Le Méhauté , A and Schumaker , LL . 209 – 246 . New York : Academic Press .
  • Jia , RQ , Lau , K and Zhou , D . 2001 . Lp solutions of refinement equations . J. Fourier Anal. Appl. , 7 : 143 – 167 .
  • Jia , RQ , Jiang , Q and Shen , Z . 2001 . Convergence of cascade algorithms associated with nonhomogeneous refinement equations . Proc. Am. Math. Soc. , 129 : 415 – 427 .
  • Jia , RQ , Jiang , Q and Shen , Z . 2000 . Distributional solutions of nonhomogeneous discrete and continuous refinement equations . SIAM J. Math. Anal. , 32 : 420 – 434 .
  • Bhatt , G , Johnson , BD and Weber , E . 2007 . Orthogonal wavelet frames and vector-valued wavelet transforms . Appl. Comput. Harmon. Anal. , 23 : 215 – 234 .
  • Bi , N , Han , B and Shen , Z . 2009 . Componentwise polynomial solutions and distribution solutions of refinement equations . Appl. Comput. Harmon. Anal. , 27 : 117 – 123 .
  • Daubechies , I and Lagarias , JC . 1991 . Two-scale difference equations. I. Existence and global regularity of solutions . SIAM J. Math. Anal. , 22 : 1388 – 1410 .
  • De Boor , C , DeVore , RA and Ron , A . 1994 . The structure of finitely generated shift-invariant spaces in L 2(ℝ d ) . J. Funct. Anal. , 119 : 37 – 78 .
  • Donovan , G , Geronimo , JS , Hardin , DP and Massopust , PR . 1996 . Construction of orthogonal wavelets using fractal interpolation functions . SIAM J. Math. Anal. , 27 : 1158 – 1192 .
  • Goodman , TNT and Lee , SL . 1994 . Wavelets of multiplicity r . Trans. Am. Math. Soc. , 342 : 307 – 324 .
  • Gu , Q and Han , D . 2005 . Super-wavelets and decomposable wavelet frames . J. Fourier Anal. Appl. , 11 : 683 – 696 .
  • Hardin , DP , Kessler , B and Massopust , PR . 1992 . Multiresolution analyses based on fractal functions . J. Approx. Theory , 71 : 104 – 120 .
  • Han , B and Jia , RQ . 2002 . Quincunx fundamental refinable functions and quincunx biorthogonal wavelets . Math. Comp. , 71 : 165 – 196 .
  • Han , B and Jia , RQ . 1998 . Multivariate refinement equations and convergence of subdivision schemes . SIAM J. Math. Anal. , 29 : 1177 – 1199 .
  • Geronimo , JS , Hardin , DP and Massopust , PR . 1994 . Fractal functions and wavelet expansions based on several scaling functions . J. Approx. Theory , 78 : 373 – 401 .
  • Hogan , TA . 1997 . Stability and linear independence of the shifts of finitely many refinable functions . J. Fourier Anal. Appl. , 3 : 757 – 774 .
  • Long , R and Chen , D . 1995 . Biorthogonal wavelet bases on ℝ d . Appl. Comput. Harmon. Anal. , 2 : 230 – 242 .
  • Lawton , W , Lee , SL and Shen , Z . 1997 . Stability and orthonormality of multivariate refinable functions . SIAM J. Math. Anal. , 28 : 999 – 1014 .
  • Li , S and Yang , J . 2007 . Vector refinement equations with infinitely supported masks . J. Approx. Theory , 148 : 158 – 176 .
  • Ron , A and Shen , Z . 2000 . The Sobolev regularity of refinable functions . J. Approx. Theory , 106 : 185 – 225 .
  • Jia , RQ and Wang , JZ . 1993 . Stability and linear independence associated with wavelet decompositions . SIAM J. Math. Anal. , 117 : 1115 – 1124 .
  • Shen , Z . 1998 . Refinable function vectors . SIAM J. Math. Anal. , 29 : 235 – 250 .
  • Jiang , Q . 1999 . Multivariate matrix refinable functions with arbitrary matrix dilation . Trans. Am. Math. Soc. , 351 : 2407 – 2438 .
  • Hogan , TA . 1998 . A note on matrix refinement equations . SIAM J. Math. Anal. , 29 : 849 – 854 .
  • Jiang , Q and Shen , Z . 1999 . On existence and weak stability of matrix refinable functions . Constr. Approx. , 15 : 337 – 353 .
  • Daubechies , I . Ten Lectures on Wavelets, Society for Industrial Mathematics, Philadelphia, 1992

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.