Rocky Mountain Journal of Mathematics

R-duality in g-frames

Farkhondeh Takhteh and Amir Khosravi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Recently, the concept of g-Riesz dual sequences for g-Bessel sequences has been introduced. In this paper, we investigate under what conditions a g-Riesz sequence $\Phi =\{\Phi _j\in L(H,H_j):j\in \mathcal I\}$ is the g-Riesz dual sequence of a given g-frame $\Lambda =\{\Lambda _i\in L(H,H_i):i\in \mathcal I\}$.

Article information

Rocky Mountain J. Math., Volume 47, Number 2 (2017), 649-665.

First available in Project Euclid: 18 April 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42C15: General harmonic expansions, frames

g-orthonormal basis g-Riesz basis g-Riesz dual sequence


Takhteh, Farkhondeh; Khosravi, Amir. R-duality in g-frames. Rocky Mountain J. Math. 47 (2017), no. 2, 649--665. doi:10.1216/RMJ-2017-47-2-649.

Export citation


  • M.R. Abdollahpour and A. Najati, Besselian g-frames and near g-Riesz bases, Appl. Anal. Disc. Math. 5 (2011), 259–270.
  • P.G. Casazza, G. Kutyniok and M.C. Lammers, Duality principles in frame theory, J. Fourier Anal. Appl. 10 (2004), 383–408.
  • O. Christensen, H.O. Kim and R.Y. Kim, On the duality principle by Casazza, Kutyniok, and Lammers, J. Fourier Anal. Appl. 17 (2011), 640–655.
  • Z. Chuang and J. Zhao, Equivalent conditions of two sequences to be R-dual, J. Inequal. Appl. 1 (2015), 1–8.
  • I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 27 (1986), 1271–1283.
  • R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341–366.
  • D. Dutkay, D. Han and D. Larson, A duality principle for groups, J. Funct. Anal. 257 (2009), 1133–1143.
  • A. Khosravi and K. Musazadeh, Fusion frames and g-frames, J. Math. Anal. Appl. 342 (2008), 1068–1083.
  • S.H. Kulkarni, Norm preserving extensions of linear operators, The Organizing Team Forays, IIT Madras, Department of Mathematics, 2016.
  • J.Z. Li and Y.C. Zhu, Exact g-frames in Hilbert spaces, J. Math. Anal. Appl. 374 (2011), 201–209.
  • E. Osgooei, A. Najati and M.H. Faroughi, G-Riesz dual sequences for g-Bessel sequences, Asian-Europ. J. Math. 7 (2014), 1450041.
  • A. Ron and Z. Shen, Weyl-Heisenberg systems and Riesz bases in $L^2(\mathbb{R}^d)$, Duke Math. J. 89 (1997), 237–282.
  • D.T. Stoeva and O. Christensen, On $R$-duals and the duality principle in Gabor analysis, J. Fourier Anal. Appl. 21 (2015), 383–400.
  • W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322 (2006), 437–452.
  • J. Wexler and S. Raz, Discrete Gabor expansions, Signal Proc. 21 (1990), 207–220.