Advanced search
Publication Cover
Numerical Functional Analysis and Optimization Volume 34, 2013 - Issue 3
Submit an article Journal homepage
177
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

The Structure of Finitely Generated Shift-Invariant Subspaces in Super Hilbert Spaces

Qingyue Zhang Department of Mathematics and LPMC, Nankai University, Tianjin, P. R. China
&
Wenchang Sun Department of Mathematics and LPMC, Nankai University, Tianjin, P. R. ChinaCorrespondence[email protected]
Pages 349-364 | Received 20 Oct 2011, Accepted 31 Jul 2012, Published online: 14 Jan 2013

REFERENCES

  • A. Aldroubi , Q. Sun , and W.S. Tang ( 2005 ). Convolution, average sampling, and a Calderon resolution of the identity for shift-invariant spaces . J. Fourier Anal. Appl. 11 : 215 – 244 .
  • M. Bownik ( 2000 ). The structure of shift-invariant subspaces of L 2(ℝ n ) . J. Funct. Anal. 177 : 282 – 309 .
  • M. Bownik and N. Kaiblinger ( 2006 ). Minimal generator sets for finitely generated shift invariant subspaces of L 2(ℝ d ) . J. Math. Anal. Appl. 313 : 342 – 352 .
  • O. Christensen ( 2003 ). An Introduction to Frames and Riesz Bases . Birkhä user , Boston .
  • C. De Boor , R. A. DeVore , and A. Ron ( 1994 ). The structure of finitely generated shift invariant spaces in L 2(ℝ d ) . J. Funct. Anal. 119 : 37 – 78 .
  • Q. Gu and D. Han ( 2005 ). Super-wavelets and decomposable wavelet frames . J. Fourier Anal. Appl. 11 : 682 – 696 .
  • R. Q. Jia ( 1998 ). Stability of the shifts of a finite number of functions . J. Approx. Theory 95 : 194 – 202 .
  • H. O. Kim , R. Y. Kim , and J. K. Lim ( 2005 ). The infimum cosine angle between two finitely generated shift-invariant spaces and its applications . Appl. Comput. Harmon. Anal. 19 : 253 – 281 .
  • H. O. Kim , R. Y. Kim , and J. K. Lim ( 2006 ). Characterization of the closedness of the sum of two shift-invariant spaces . Appl. Comput. Harmon. Anal. 320 : 381 – 395 .
  • J. M. Kim and K. H. Kwon ( 2008 ). Vector sampling expansion in Riesz bases setting and its aliasing error . Appl. Comput. Harmon. Anal. 25 : 315 – 334 .
  • A. Ron and Z. Shen ( 1995 ). Frames and stable bases for shift-invariant subspaces of L 2(ℝ d ) . Canad. J. Math. 47 : 1051 – 1094 .
  • 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 .
  • O. Rudolph ( 2000 ). Super Hilbert Spaces . Commun. Math. Phys. 214 : 449 – 467 .
  • A. Ron and Z. Shen ( 2005 ). Generalized shift-invariant systems . Constr. Approx. 22 : 1 – 45 .
  • Z. Shang , W. Sun , and X. Zhou ( 2007 ). Vector sampling expansions in shift invariant subspaces . J. Math. Anal. Appl. 325 : 898 – 919 .
  • Z. Wu ( 2002 ). The Shift-Invariant Subspaces in L 1(ℝ) . J. Approx. Theory 118 : 81 – 93 .
  • E. Weber ( 2004 ). Orthogonal frames of translates . Appl. Comput. Harmon. Anal. 17 : 69 – 90 .
  • L. Zang , W. Sun , and D. Chen ( 2009 ). Excess of a class of g-frames . J. Math. Anal. Appl. 252 : 711 – 717 .

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.