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Year 2020, Volume: 49 Issue: 4, 1295 - 1302, 06.08.2020
https://doi.org/10.15672/hujms.667404

Abstract

References

  • [1] P. G. Cassaza and M. T. Leon, Projections of frames, Proc. SPIE 5914, 591402, 277- 289, 2005. Doi: 10.1117/12.615278.
  • [2] R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72, 341-366, 1952.
  • [3] X. X. Guo, New Characterizations of g-Bessel Sequences and g-Riesz Bases in Hilbert Spaces, Result Math. 68, 361-374, 2015.
  • [4] A. Najati, M. H. Faroughi and A. Rahimi, G-frames and stability of g-frames in Hilbert spaces, Methods Func. Anal. Topology 4, 271-286, 2008.
  • [5] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322, 437-452, 2006.
  • [6] X. C. Xiao, G. R. Zhou and Y. C. Zhu, Weaving of K-g-frames in Hilbert spaces, Science Asia 45, 285- 291, 2019.
  • [7] X. C. Xiao, Y. C. Zhu and G. R. Zhou, Characterizations of (near) exact g-frames, g-Riesz bases and Besselian g-frames, Int. J. Wavelets Multiresolut. Inf. Process. 17 (5), 1950040, 2019, https://doi.org/10.1142/S0219691319500401.

Eigenvalues and eigenvectors for a $G$-frame operator

Year 2020, Volume: 49 Issue: 4, 1295 - 1302, 06.08.2020
https://doi.org/10.15672/hujms.667404

Abstract

In this paper, we investigate eigenvalues and eigenvectors of the $g$-frame operator of $\{\Lambda_jP\in B(K,H_j):j\in\mathbb{J}\}$, where $\{\Lambda_j\in B(H,H_j): j\in\mathbb{J}\}$ is a $g$-frame for an $N$-dimensional Hilbert space $H$ and $P$ is a rank $k$ orthogonal projection of $H$ onto $K,$ a closed subspace of $H$.

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References

  • [1] P. G. Cassaza and M. T. Leon, Projections of frames, Proc. SPIE 5914, 591402, 277- 289, 2005. Doi: 10.1117/12.615278.
  • [2] R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72, 341-366, 1952.
  • [3] X. X. Guo, New Characterizations of g-Bessel Sequences and g-Riesz Bases in Hilbert Spaces, Result Math. 68, 361-374, 2015.
  • [4] A. Najati, M. H. Faroughi and A. Rahimi, G-frames and stability of g-frames in Hilbert spaces, Methods Func. Anal. Topology 4, 271-286, 2008.
  • [5] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322, 437-452, 2006.
  • [6] X. C. Xiao, G. R. Zhou and Y. C. Zhu, Weaving of K-g-frames in Hilbert spaces, Science Asia 45, 285- 291, 2019.
  • [7] X. C. Xiao, Y. C. Zhu and G. R. Zhou, Characterizations of (near) exact g-frames, g-Riesz bases and Besselian g-frames, Int. J. Wavelets Multiresolut. Inf. Process. 17 (5), 1950040, 2019, https://doi.org/10.1142/S0219691319500401.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Azam Yousefzadeheyni This is me 0000-0003-1102-7877

Mohammad Reza Abdollahpour This is me 0000-0001-9480-4111

Publication Date August 6, 2020
Published in Issue Year 2020 Volume: 49 Issue: 4

Cite

APA Yousefzadeheyni, A., & Abdollahpour, M. R. (2020). Eigenvalues and eigenvectors for a $G$-frame operator. Hacettepe Journal of Mathematics and Statistics, 49(4), 1295-1302. https://doi.org/10.15672/hujms.667404
AMA Yousefzadeheyni A, Abdollahpour MR. Eigenvalues and eigenvectors for a $G$-frame operator. Hacettepe Journal of Mathematics and Statistics. August 2020;49(4):1295-1302. doi:10.15672/hujms.667404
Chicago Yousefzadeheyni, Azam, and Mohammad Reza Abdollahpour. “Eigenvalues and Eigenvectors for a $G$-Frame Operator”. Hacettepe Journal of Mathematics and Statistics 49, no. 4 (August 2020): 1295-1302. https://doi.org/10.15672/hujms.667404.
EndNote Yousefzadeheyni A, Abdollahpour MR (August 1, 2020) Eigenvalues and eigenvectors for a $G$-frame operator. Hacettepe Journal of Mathematics and Statistics 49 4 1295–1302.
IEEE A. Yousefzadeheyni and M. R. Abdollahpour, “Eigenvalues and eigenvectors for a $G$-frame operator”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, pp. 1295–1302, 2020, doi: 10.15672/hujms.667404.
ISNAD Yousefzadeheyni, Azam - Abdollahpour, Mohammad Reza. “Eigenvalues and Eigenvectors for a $G$-Frame Operator”. Hacettepe Journal of Mathematics and Statistics 49/4 (August 2020), 1295-1302. https://doi.org/10.15672/hujms.667404.
JAMA Yousefzadeheyni A, Abdollahpour MR. Eigenvalues and eigenvectors for a $G$-frame operator. Hacettepe Journal of Mathematics and Statistics. 2020;49:1295–1302.
MLA Yousefzadeheyni, Azam and Mohammad Reza Abdollahpour. “Eigenvalues and Eigenvectors for a $G$-Frame Operator”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, 2020, pp. 1295-02, doi:10.15672/hujms.667404.
Vancouver Yousefzadeheyni A, Abdollahpour MR. Eigenvalues and eigenvectors for a $G$-frame operator. Hacettepe Journal of Mathematics and Statistics. 2020;49(4):1295-302.