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Abstract

In this paper, we give some sufficient conditions under which perturbations preserve ℓ p -localized frames. Using an arbitrary given sequence, we provide a simple way for constructing ℓ p -localized sequences.

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References

  1. R. Balan, P. G. Casazza, C. Heil, and Z. Landau, “Density, overcompleteness, and localization of frames”, AMS Electronic Research Announcements, 12, 71–86, 2006.

    MathSciNet  MATH  Google Scholar 

  2. R. Balan, P. G. Casazza, C. Heil, and Z. Landau, “Density, overcompleteness, and localization of frames, 1. Theory”, J. Fourier Anal. Appl., 12 (2), 105–143, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Balan, P. G. Casazza, C. Heil, and Z. Landau, “Density, overcompleteness, and localization of frames, 2. Gabor systems”, J. Fourier Anal. Appl., 12 (3), 309–344, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  4. O. Christensen, An Introduction to Frames and Riesz Bases (Birkhaüser, Basel, 2002).

    MATH  Google Scholar 

  5. O. Christensen, “A Paley Wiener theorem for frames”, Proc. Amer.Math. Soc., 123, 256–270, 1995.

    MathSciNet  MATH  Google Scholar 

  6. R. I. Duffin and A. C. Schaeffer, “A class of nonharmonic Fourier series”, Trans. Amer.Math. Soc. 72, 341–366, 1952.

    Article  MathSciNet  MATH  Google Scholar 

  7. C. Heil, D. Walnut, “Continuous and discrete wavelet transform”, SIAMRev., 31, 628–666, 1969.

    MATH  Google Scholar 

  8. R. Paley and N. Wiener, “Fourier transform in complex domains”, AMS Colloquium Publications, 19, 1934.

  9. R. Young, An Introduction to Nonharmonic Fourier Series (Academic Press, New York, 1980).

    MATH  Google Scholar 

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Correspondence to M. A. Hasankhani Fard.

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Original Russian Text © M. A. Hasankhani Fard, 2018, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2018, No. 2, pp. 75–82.

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Hasankhani Fard, M.A. On Perturbations of ℓ p -localized Frames. J. Contemp. Mathemat. Anal. 53, 71–76 (2018). https://doi.org/10.3103/S1068362318020024

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  • DOI: https://doi.org/10.3103/S1068362318020024

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