Eigenvalues and Eigenvectors for a Continuous G-Frame Operator

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DOI: https://doi.org/10.28924/2291-8639-22-2024-88
Published: May 27, 2024
Cite as:
Hamid Faraj, M. Maghfoul, Eigenvalues and Eigenvectors for a Continuous G-Frame Operator, Int. J. Anal. Appl., 22 (2024), 88.

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Hamid Faraj, M. Maghfoul

Abstract

In this paper, we give a simple characterization of the eigenvalues and eigenvectors for the continous G-frame operator for {ΛωP∈B(H,Kω), ω∈Ω}, where HN is an N-dimensional Hilbert space and P is a rank k orthogonal projection on HN. Using this, we derive several results.

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References

  1. M.R. Abdollahpour, M.H. Faroughi, Continuous G-Frames in Hilbert Spaces, Southeast Asian Bull. Math. 32 (2008), 1–19.
  2. A. Yousefzadeheyni, M.R. Abdollahpour, Eigenvalues and Eigenvectors for a G-Frame Operator, Hacettepe J. Math. Stat. 49 (2020), 1295–1302. https://doi.org/10.15672/hujms.667404.
  3. P.G. Casazza, The Art of Frame Theory, Taiwan. J. Math. 4 (2000), 129–201. https://www.jstor.org/stable/43834412.
  4. P.G. Casazza, G. Kutyniok, F. Philipp, Introduction to Finite Frame Theory, in: P.G. Casazza, G. Kutyniok (Eds.), Finite Frames, Birkhäuser Boston, Boston, 2013: pp. 1–53. https://doi.org/10.1007/978-0-8176-8373-3_1.
  5. O. Christensen, An Introduction to Frames and Riesz Bases, Springer, Cham, 2016. https://doi.org/10.1007/978-3-319-25613-9.
  6. I. Daubechies, A. Grossmann, Y. Meyer, Painless Nonorthogonal Expansions, J. Math. Phys. 27 (1986), 1271–1283. https://doi.org/10.1063/1.527388.
  7. R.J. Duffin, A.C. Schaeffer, A Class of Nonharmonic Fourier Series, Trans. Amer. Math. Soc. 72 (1952), 341–366.
  8. K. Gro¨chenig, Foundations of Time-Frequency Analysis, Birkhauser, Boston, 2001.
  9. T. Strohmer, R.W. Heath Jr., Grassmannian Frames With Applications to Coding and Communication, Appl. Comp. Harm. Anal. 14 (2003), 257–275. https://doi.org/10.1016/s1063-5203(03)00023-x.
  10. W. Sun, G-Frames and g-Riesz Bases, J. Math. Anal. Appl. 322 (2006), 437–452. https://doi.org/10.1016/j.jmaa.2005.09.039.