About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 923729, 14 pages
http://dx.doi.org/10.1155/2012/923729
Research Article

-Bases in Hilbert Spaces

Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China

Received 13 October 2012; Accepted 3 December 2012

Academic Editor: Wenchang Sun

Copyright © 2012 Xunxiang Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Gabor, “Theory of communications,” Journal of the American Institute of Electrical Engineers, vol. 93, pp. 429–457, 1946.
  2. R. J. Duffin and A. C. Schaeffer, “A class of nonharmonic Fourier series,” Transactions of the American Mathematical Society, vol. 72, pp. 341–366, 1952. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. I. Daubechies, A. Grossmann, and Y. Meyer, “Painless nonorthogonal expansions,” Journal of Mathematical Physics, vol. 27, no. 5, pp. 1271–1283, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. D. Han and D. R. Larson, “Frames, bases and group representations,” Memoirs of the American Mathematical Society, vol. 147, no. 697, p. 7, 2000. View at Zentralblatt MATH
  5. O. Christensen, An Introduction to Frames and Riesz Bases, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, Mass, USA, 2003.
  6. I. Daubechies, Ten Lectures on Wavelets, vol. 61, SIAM, Philadelphia, Pa, USA, 1992. View at Publisher · View at Google Scholar
  7. C. E. Heil and D. F. Walnut, “Continuous and discrete wavelet transforms,” SIAM Review, vol. 31, no. 4, pp. 628–666, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. H. G. Feichtinger and T. Strohmer, Gabor Analysis and Algorithms, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, Mass, USA, 1998.
  9. M. Frazier and B. Jawerth, “Decomposition of Besov spaces,” Indiana University Mathematics Journal, vol. 34, no. 4, pp. 777–799, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. K. Gröchenig, “Describing functions: atomic decompositions versus frames,” Monatshefte für Mathematik, vol. 112, no. 1, pp. 1–42, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. W. Sun, “G-frames and g-Riesz bases,” Journal of Mathematical Analysis and Applications, vol. 322, no. 1, pp. 437–452, 2006. View at Publisher · View at Google Scholar
  12. Y. C. Zhu, “Characterizations of g-frames and g-Riesz bases in Hilbert spaces,” Acta Mathematica Sinica, vol. 24, no. 10, pp. 1727–1736, 2008. View at Publisher · View at Google Scholar
  13. A. Najati, M. H. Faroughi, and A. Rahimi, “G-frames and stability of g-frames in Hilbert spaces,” Methods of Functional Analysis and Topology, vol. 14, no. 3, pp. 271–286, 2008.
  14. Y. J. Wang and Y. C. Zhu, “G-frames and g-frame sequences in Hilbert spaces,” Acta Mathematica Sinica, vol. 25, no. 12, pp. 2093–2106, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. A. Khosravi and K. Musazadeh, “Fusion frames and g-frames,” Journal of Mathematical Analysis and Applications, vol. 342, no. 2, pp. 1068–1083, 2008. View at Publisher · View at Google Scholar
  16. M. L. Ding and Y. C. Zhu, “G-Besselian frames in Hilbert spaces,” Acta Mathematica Sinica, vol. 26, no. 11, pp. 2117–2130, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. A. Abdollahi and E. Rahimi, “Some results on g-frames in Hilbert spaces,” Turkish Journal of Mathematics, vol. 35, no. 4, pp. 695–704, 2011. View at Zentralblatt MATH