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Indian Journal of Pure and Applied Mathematics

, Volume 50, Issue 4, pp 863–875 | Cite as

Continuous controlled K-g-frames in Hilbert spaces

  • R. RezapourEmail author
  • A. RahimiEmail author
  • E. OsgooeiEmail author
  • H. DehghanEmail author
Article
  • 18 Downloads

Abstract

In this paper, we introduce the concept of continuous controlled K-g-frames which are generalizations of discrete controlled K-g-frames. These frames include many of previous generalizations of frames. We discuss characterizations of continuous controlled K-g-frames in Hilbert spaces. Finally, we propose several methods to construct such frames.

Key words

Controlled K-g-frames continuous frame g-Bessel sequences frame operator 

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Notes

Acknowledgement

The authors would like to thanks Professor M. H. Faroughi for his comments and suggestions. Also, they would like to thank the reviewers for their valuable comments.

References

  1. 1.
    M. R. Abdollahpour and M. H. Faroughi, Continuous G-frames in Hilbert spaces, Southeast Asian Bull. Math., 32 (2008), 1–19.MathSciNetzbMATHGoogle Scholar
  2. 2.
    M. S. Asgari, H. Rahimi, Generalized frames for operators in Hilbert spaces, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 17(2) (2014), 1469–1477.MathSciNetCrossRefGoogle Scholar
  3. 3.
    S. H. Avazzadeh, R. A. Kamyabi Gol, and R. Raisi Tousi, Continuous frames and g-frames, Bull. Iranian Math. Soc., 40 (2014), 1047–1055.MathSciNetzbMATHGoogle Scholar
  4. 4.
    P. Balazs, J. P. Antoine, and A. Grybos, Weighted and controlled frames, Int. J. Wavelets Multiresolut. Inf. Process., 8(1) (2010), 109–132MathSciNetCrossRefGoogle Scholar
  5. 5.
    I. Bogdanova, P. Vandergheynst, J. P. Antoine, L. Jacquesb, and M. Morvidone, Stereographic wavelet frames on the sphere, Appl. Comput. Harmon. Anal., 19(2) (2005), 23–252.MathSciNetCrossRefGoogle Scholar
  6. 6.
    O. Christensen, An introduction to frames and Riesz bases, Birkhauser, Boston (2016).zbMATHGoogle Scholar
  7. 7.
    I. Daubechies, A. Grossman, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27(5) (1986), 1271–1283.MathSciNetCrossRefGoogle Scholar
  8. 8.
    R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Am. Math. Soc., 17(2) (1966), 413–415.MathSciNetCrossRefGoogle Scholar
  9. 9.
    R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Am. Math. Soc., 72 (1952), 341–366.MathSciNetCrossRefGoogle Scholar
  10. 10.
    M. H. Faroughi and M. Rahmani, Bochner p-g-frames, J. Inequal. Appl., 5 (2012), 1–16.MathSciNetzbMATHGoogle Scholar
  11. 11.
    H. G. Feichtinger and T. Werther, Atomic systems for subspaces, In: Zayed, L. (ed.) Proceedings SampTA 2001, Orlando, (2001), 163–165.Google Scholar
  12. 12.
    L. Gavruta, Frames for operators, Appl. Comput. Harmon. Anal., 32(1) (2012), 139–144.MathSciNetCrossRefGoogle Scholar
  13. 13.
    L. Gavruta, New results on frames for operators, Analele Universitatii Oradea Fasc. Matematica, Tom XIX(2) (2012), 55–61.MathSciNetzbMATHGoogle Scholar
  14. 14.
    D. Hua and Y. Huang, Controlled K-g-frames in Hilbert spaces, Results. Math., 72(3) (2017), 1227–1238.MathSciNetCrossRefGoogle Scholar
  15. 15.
    G. J. Murphy, C*-algebras and operator theory, Acadamic Press Inc., (1990).zbMATHGoogle Scholar
  16. 16.
    W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl., 322(1) (2006), 437–452.MathSciNetCrossRefGoogle Scholar
  17. 17.
    X. Xiao, Y. Zhu, and L. Gavruta, Some properties of K-frames in Hilbert spaces, Results Math., 63(3–4) (2013), 1243–1255.MathSciNetCrossRefGoogle Scholar

Copyright information

© Indian National Science Academy 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Shabestar BranchIslamic Azad UniversityShaberstarIran
  2. 2.Department of MathematicsUniversity of MaraghehMaraghehIran
  3. 3.Department of SciencesUrmia University of TechnologyUrmiaIran
  4. 4.Department of MathematicsInstitute for Advanced Studies in Basic Sciences (IASBS)Gava Zang, ZanjanIran

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