| | | |

Eigenvalues and eigenvectors for a $G$-frame operator

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 $H$.

***************************************************************************************************************

***************************************************************************************************************

Eigenvalue, eigenvector, g-frame, g-frame operator, tight g-frame
• [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.
Primary Language en Mathematics Mathematics Orcid: 0000-0003-1102-7877Author: Azam YOUSEFZADEHEYNİ Institution: University of Mohaghegh ArdabiliCountry: Iran Orcid: 0000-0001-9480-4111Author: Mohammad Reza ABDOLLAHPOUR (Primary Author)Institution: University of Mohaghegh ArdabiliCountry: Iran Publication Date : August 6, 2020
 Bibtex @research article { hujms667404, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1295 - 1302}, doi = {10.15672/hujms.667404}, title = {Eigenvalues and eigenvectors for a \$G\$-frame operator}, key = {cite}, author = {Yousefzadeheyni̇, Azam and Abdollahpour, Mohammad Reza} } APA Yousefzadeheyni̇, A , Abdollahpour, M . (2020). Eigenvalues and eigenvectors for a $G$-frame operator . Hacettepe Journal of Mathematics and Statistics , 49 (4) , 1295-1302 . DOI: 10.15672/hujms.667404 MLA Yousefzadeheyni̇, A , Abdollahpour, M . "Eigenvalues and eigenvectors for a $G$-frame operator" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1295-1302 Chicago Yousefzadeheyni̇, A , Abdollahpour, M . "Eigenvalues and eigenvectors for a $G$-frame operator". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1295-1302 RIS TY - JOUR T1 - Eigenvalues and eigenvectors for a $G$-frame operator AU - Azam Yousefzadeheyni̇ , Mohammad Reza Abdollahpour Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.667404 DO - 10.15672/hujms.667404 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1295 EP - 1302 VL - 49 IS - 4 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.667404 UR - https://doi.org/10.15672/hujms.667404 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Eigenvalues and eigenvectors for a $G$-frame operator %A Azam Yousefzadeheyni̇ , Mohammad Reza Abdollahpour %T Eigenvalues and eigenvectors for a $G$-frame operator %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 4 %R doi: 10.15672/hujms.667404 %U 10.15672/hujms.667404 ISNAD Yousefzadeheyni̇, 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 AMA Yousefzadeheyni̇ A , Abdollahpour M . Eigenvalues and eigenvectors for a $G$-frame operator. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1295-1302. Vancouver Yousefzadeheyni̇ A , Abdollahpour M . Eigenvalues and eigenvectors for a $G$-frame operator. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1295-1302.

Authors of the Article
[1]
[2]