DOI QR코드

DOI QR Code

G-frames as Sums of Some g-orthonormal Bases

  • Abdollahpour, Mohammad Reza (Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili) ;
  • Najati, Abbas (Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili)
  • 투고 : 2011.05.14
  • 심사 : 2011.09.28
  • 발행 : 2013.03.23

초록

In this paper we show that a $g$-frame for a Hilbert space $\mathcal{H}$ can be written as a linear combination of two $g$-orthonormal bases for $\mathcal{H}$ if and only if it is a $g$-Riesz basis for $\mathcal{H}$. Also, we show that every $g$-frame for a Hilbert space $\mathcal{H}$ is a multiple of a sum of three $g$-orthonormal bases for $\mathcal{H}$.

키워드

참고문헌

  1. P. G. Casazza, Every frames is a sum of three (but not two) orthonormal bases- and other frame representations, J. Fourier Anal. Appl., 4(1998), 727-732. https://doi.org/10.1007/BF02479676
  2. P. G. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math., 345(2004), 87-113. https://doi.org/10.1090/conm/345/06242
  3. O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, Boston, 2003.
  4. O. Christensen and Y. C. Eldar, Oblique dual frames and shift invariant-spaces, Appl. Comput. Harmon. Anal., 17(2004), 48-68. https://doi.org/10.1016/j.acha.2003.12.003
  5. R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72(1952), 341-366. https://doi.org/10.1090/S0002-9947-1952-0047179-6
  6. M. Fornasier, Decompositions of Hibert space: local construction of global frames, Proc. Int. Conf. On Constructive Function Theory, varna(2002), B. Bojanov Ed., DARBA, Sofia, 2003, 275-281.
  7. S. Li and H. Ogawa, Pseudoframes for subspaces with applications, J. Fourier Anal. Appl., 10(2004), 409-431. https://doi.org/10.1007/s00041-004-3039-0
  8. A. Najati, M. H. Faroughi and A. Rahimi, G-frames and stability of g-frames in Hilbert spaces, Methods Funct. Anal. Topology, 4(2008), 271-286.
  9. S. Obeidat, S. Samarah, P. G. Casazza and J. C. Tremain, Sums of Hilbert Space frames, J. Math. Anal. Appl., 351(2009), 579-585. https://doi.org/10.1016/j.jmaa.2008.10.040
  10. W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl., 322(2006), 437-452. https://doi.org/10.1016/j.jmaa.2005.09.039