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G-frames as Sums of Some g-orthonormal Bases
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  • Journal title : Kyungpook mathematical journal
  • Volume 53, Issue 1,  2013, pp.135-141
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2013.53.1.135
 Title & Authors
G-frames as Sums of Some g-orthonormal Bases
Abdollahpour, Mohammad Reza; Najati, Abbas;
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 Abstract
In this paper we show that a -frame for a Hilbert space can be written as a linear combination of two -orthonormal bases for if and only if it is a -Riesz basis for . Also, we show that every -frame for a Hilbert space is a multiple of a sum of three -orthonormal bases for .
 Keywords
g-Bessel sequence;g-frame;g-orthonormal basis;g-Riesz basis;
 Language
English
 Cited by
 References
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. crossref(new window)

2.
P. G. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math., 345(2004), 87-113. crossref(new window)

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. crossref(new window)

5.
R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72(1952), 341-366. crossref(new window)

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. crossref(new window)

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. crossref(new window)

10.
W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl., 322(2006), 437-452. crossref(new window)