Skip to main content
Log in

Necessary condition and sufficient condition for affine frames

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

The main goal of this paper is to establish a set of necessary conditions for affine frames. These conditions are also sufficient for tight frames.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Daubechies, I., The wavelet transform time-frequency localization and signal analysis, IEEE Trans. Inform. Theory, 1990, 36: 961–1005.

    Article  MATH  MathSciNet  Google Scholar 

  2. Chui, C. K., Shi, X. L., Inequalities of Littlewood-Paley type for frames and wavelets, SIAM. J. Math. Anal., 1993, 24: 263–277.

    Article  MATH  MathSciNet  Google Scholar 

  3. Chui, C. K., An Introduction to Wavelets, Boston: Academic Press, 1992.

    MATH  Google Scholar 

  4. Daubechies, I., Ten Lectures on Wavelets, CBMS-NSF Series in Applied Math., Vol. 61, Philadelphia: SIAM, 1992.

    Google Scholar 

  5. Kahane, J., Lemarie’-Rieusset, P. G., Fourier Series and Wavelets, France: Gordon and Breach Publishers, 1994.

    Google Scholar 

  6. Kaiser, G., Friendly, A., Guide to Wavelets, Berlin, Boston: Birkhauser, 1994.

    MATH  Google Scholar 

  7. Christensen, O., An Introduction to Frames and Riese Bases, Boston: Birkhauser, 2002.

    Google Scholar 

  8. Shi, X. L., Shi, Q. L., New criterion on affine frames, Chinese Annals of Math., 2005, 26A(2): 257–262.

    Google Scholar 

  9. Chui, C. K., Shi, X. L., Orthonormal wavelets and tight frames with arbitrary real dilations, Appl. Comput. Harmon. Anal., 2000, 9: 243–264.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shi Xianliang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shi, X., Chen, F. Necessary condition and sufficient condition for affine frames. Sci. China Ser. A-Math. 48, 1369–1378 (2005). https://doi.org/10.1360/04ys0143

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1360/04ys0143

Keywords

Navigation