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Journal of Mathematics
Volume 2013, Article ID 318659, 4 pages
http://dx.doi.org/10.1155/2013/318659
Research Article

On Schauder Frames in Conjugate Banach Spaces

1Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110 007, India
2Department of Mathematics, Motilal Nehru College, University of Delhi, Delhi 110 021, India

Received 31 August 2012; Accepted 17 November 2012

Academic Editor: Ding-Xuan Zhou

Copyright © 2013 S. K. Kaushik et al. 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. 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 · View at MathSciNet
  2. I. Daubechies, A. Grossmann, and Y. Meyer, “Painless non-orthogonal expansions,” Journal of Mathematical Physics, vol. 27, no. 5, pp. 1271–1283, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. Li and H. Ogawa, “Pseudo-duals of frames with applications,” Applied and Computational Harmonic Analysis, vol. 11, no. 2, pp. 289–304, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. O. Christensen and Y. C. Eldar, “Oblique dual frames and shift-invariant spaces,” Applied and Computational Harmonic Analysis, vol. 17, no. 1, pp. 48–68, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. G. Casazza and G. Kutyniok, “Frames of subspaces,” in Wavelets, Frames and Operator Theory, vol. 345 of Contemporary Mathematics, pp. 87–113, American Mathematical Society, Providence, RI, USA, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. 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
  7. Virender, A. Zothansanga, and S. K. Kaushik, “On almost orthogonal frames,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 920607, 6 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. Liu, G. Hu, and G. Wu, “Orthogonal multiwavelet frames in L2(Rd),” Journal of Applied Mathematics, vol. 2012, Article ID 846852, 18 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. G. Feichtinger and K. Gröchenig, “A unified approach to atomic decompositions via integrable group representations,” in Proceedings of the Function Spaces and Applications, vol. 1302 of Lecture Notes in Mathematics, pp. 52–73, Springer, New York, NY, USA, 1988. View at Zentralblatt MATH · View at MathSciNet
  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 · View at MathSciNet
  11. O. Christensen and C. Heil, “Perturbations of Banach frames and atomic decompositions,” Mathematische Nachrichten, vol. 185, pp. 33–47, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. K. Jain, S. K. Kaushik, and L. K. Vashisht, “On Banach frames,” Indian Journal of Pure and Applied Mathematics, vol. 37, no. 5, pp. 265–272, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. S. K. Kaushik and S. K. Sharma, “On approximative atomic decompositions in Banach spaces,” Communications in Mathematics and Applications, vol. 3, no. 3, pp. 293–301, 2012. View at Google Scholar
  14. S. K. Kaushik and S. K. Sharma, “On a generalization of atomic decompositions,” Albanian Journal of Mathematics, vol. 5, no. 1, pp. 21–29, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. Han and D. R. Larson, Frames Bases and Group Representations, vol. 147 of Memoirs of the American Mathematical Society, 2000. View at Zentralblatt MATH · View at MathSciNet
  16. P. G. Casazza, D. Han, and D. R. Larson, “Frames for Banach spaces,” Contemporary Mathematics, vol. 247, pp. 149–182, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. P. G. Casazza, S. J. Dilworth, E. Odell, Th. Schlumprecht, and A. Zsák, “Coefficient quantization for frames in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 348, no. 1, pp. 66–86, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. R. Liu, “On shrinking and boundedly complete Schauder frames of Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 365, no. 1, pp. 385–398, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R. Liu and B. Zheng, “A characterization of Schauder frames which are near-Schauder bases,” The Journal of Fourier Analysis and Applications, vol. 16, no. 5, pp. 791–803, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. R. Holub, “Pre-frame operators, Besselian frames, and near-Riesz bases in Hilbert spaces,” Proceedings of the American Mathematical Society, vol. 122, no. 3, pp. 779–785, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. K. Beanland, D. Freeman, and R. Liu, “Upper and lower estimates for Schauder frames and atomic decompositions,” In press, http://arxiv.org/abs/1202.2492v1.
  22. L. K. Vashisht, “On Φ-Schauder frames,” TWMS Journal of Applied and Engineering Mathematics, vol. 2, no. 1, pp. 116–120, 2012. View at Google Scholar
  23. R. Liu, “Hilbert-Schauder frame operators,” Operators and Matrices, vol. 7, no. 1, pp. 91–99, 2013. View at Google Scholar
  24. P. K. Jain, S. K. Kaushik, and L. K. Vashisht, “Banach frames for conjugate Banach spaces,” Zeitschrift für Analysis und ihre Anwendungen, vol. 23, no. 4, pp. 713–720, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. M. Day, Normed Linear Spaces, Springer, Berlin, Germany, 1958.