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On Constructions of Kg-Frames in Hilbert Spaces

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Abstract

One of the most important problems in the studying of frames and its extensions is the invariance of these systems under perturbation. In this paper, we first give a result concerning perturbations of Kg-frames and then use it to construct Kg-frames in Hilbert spaces. We also characterize the concept of Kg-frames by quotient maps.

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References

  1. Bellomonte, G., Corso, R.: Frames and weak frames for unbounded operators. Adv. Comput. Math. 46(38), 1–21 (2020)

    MathSciNet  MATH  Google Scholar 

  2. Conway, J.B.: A Course in Functional Analysis, 2nd edn. Springer, New York (1990)

    MATH  Google Scholar 

  3. Douglas, R.G.: On majorization, factorization, and range inclusion of operators on Hilbert space. Proc. Am. Math. Soc. 17, 413–415 (1966)

    Article  MathSciNet  Google Scholar 

  4. Du, D., Zhu, Y.C.: Constructions of \(K\)-\(g\)-frames and tight \(K\)-\(g\)-frames in Hilbert spaces. Bull. Malays. Math. Sci. Soc. 34(4), 4107–4122 (2020)

    Article  MathSciNet  Google Scholar 

  5. Duffin, R.J., Schaeffer, A.C.: A class of nonharmonic Fourier series. Trans. Am. Math. Soc. 72, 341–366 (1952)

    Article  MathSciNet  Google Scholar 

  6. Gavruta, L.: Frames for operators. Appl. Comput. Harmon. Anal. 32, 139–144 (2012)

    Article  MathSciNet  Google Scholar 

  7. Guo, X.: Perturbations of invertible operators and stability of \(g\)-frames in Hilbert spaces. Results Math. 64, 405–421 (2013)

    Article  MathSciNet  Google Scholar 

  8. He, M., Leng, J., Yu, J., Xu, Y.: On the sum of \(K\)-frames in Hilbert spaces. Mediterr. J. Math. 46, 2–19 (2020)

    MathSciNet  MATH  Google Scholar 

  9. Hewitt, E., Ross, K.A.: Abstract Harmonic Analysis. Springer, New York (1979)

    Book  Google Scholar 

  10. Hua, D., Huang, Y.: \(K\)-\(g\)-frames and stability of \(K\)-\(g\)-frames in Hilbert spaces. J. Korean Math. Soc. 53(6), 1331–1345 (2016)

    Article  MathSciNet  Google Scholar 

  11. Huang, Y., Hua, D.: Tight \(K\)-\(g\)-frames and its novel characterizations via atomic systems. Adv. Math. Phys. Article 3783456 (2016)

  12. Huang, Y., Shi, S.: New constructions of \(K\)-\(g\)-frames. Result Math. 73, 1–13 (2018). https://doi.org/10.1007/S00025-018-0924-4

    Article  MathSciNet  MATH  Google Scholar 

  13. Khosravi, A., Mirzaee Azandaryani, M.: Approximation of \(g\)-frames in Hilbert spaces. Acta Math. Sci. 34B(3), 639–652 (2014)

    Article  Google Scholar 

  14. Shi, S., Huang, Y.: \(K\)-\(g\)-frames and their dual. Int. J. Wavelets Multiresolut. Inf. Process. 17(1), 1–11 (2019)

    Article  MathSciNet  Google Scholar 

  15. Sun, W.: \(G\)-frames and \(g\)-Riesz bases. J. Math. Anal. Appl. 322(1), 437–452 (2006)

    Article  MathSciNet  Google Scholar 

  16. Sun, W.: Stability of \(g\)-frames. J. Math. Anal. Appl. 326(2), 858–868 (2006)

    Article  MathSciNet  Google Scholar 

  17. Xiang, Z.: Canonical dual \(K\)-\(g\)-Bessel sequences and \(K\)-\(g\)-frame sequences. Results Math. 73, 3–19 (2019)

    MathSciNet  Google Scholar 

  18. Xiang, Z.: Some new results on the construction and stability of \(K\)-\(g\)-frames in Hilbert spaces. Int. J. Wavelets Multiresolut. Inf. Process. 18(5), 1–19 (2020)

    Article  MathSciNet  Google Scholar 

  19. Xiao, X., Zhu, Y.: Exact \(K\)-\(g\)-frames in Hilbert spaces. Results Math. 72, 1329–1339 (2017)

    Article  MathSciNet  Google Scholar 

  20. Xiao, X., Zhu, Y., Gavruta, Y.: Some properties of \(K\)-frames in Hilbert spaces. Results Math. 63(4), 1243–1255 (2013)

    Article  MathSciNet  Google Scholar 

  21. Xiao, X., Zhu, Y., Shu, Z., Ding, M.: \(G\)-frames with bounded linear operators. Rocky Mt. J. Math. 45(2), 675–693 (2015)

    Article  MathSciNet  Google Scholar 

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Javadi, F., Mehdipour, M.J. On Constructions of Kg-Frames in Hilbert Spaces. Mediterr. J. Math. 18, 210 (2021). https://doi.org/10.1007/s00009-021-01862-x

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  • DOI: https://doi.org/10.1007/s00009-021-01862-x

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