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 $H$.******************************************************************************************************************************************************************************************************************************
📌 3 Maddede Bu Makale
🎯
Amaç & Hipotez: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 $H$.******************************************************************************************************************************************************************************************************************************
📊
Temel Bulgular & Veri: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 $H$.******************************************************************************************************************************************************************************************************************************
💡
Sonuç & Katkı: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 $H$.******************************************************************************************************************************************************************************************************************************
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Eigenvalue · eigenvector · g-frame
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 $H$.******************************************************************************************************************************************************************************************************************************
Yousefzadeheyni, A., Abdollahpour, M. R. (2022). Eigenvalues and eigenvectors for a $G$-frame operator. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 4, 1295–1302. https://ajindex.com/articles/529610
P. G. Cassaza and M. T. Leon, Projections of frames, Proc. SPIE 5914, 591402, 277- 289, 2005. Doi: 10.1117/12.615278
R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72, 341-366, 1952
X. X. Guo, New Characterizations of g-Bessel Sequences and g-Riesz Bases in Hilbert Spaces, Result Math. 68, 361-374, 2015
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
W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322, 437-452, 2006
X. C. Xiao, G. R. Zhou and Y. C. Zhu, Weaving of K-g-frames in Hilbert spaces, Science Asia 45, 285- 291, 2019
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.