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DOI QR Code

FRAME OPERATORS AND SEMI-FRAME OPERATORS OF FINITE GABOR FRAMES

  • Namboothiri, N.M. Madhavan (Department of Mathematics, Government College Kottayam) ;
  • Nambudiri, T.C. Easwaran (Department of Mathematics, Government Brennen College Thalassery) ;
  • Thomas, Jineesh (St. Thomas College Palai)
  • Received : 2021.03.16
  • Accepted : 2021.09.25
  • Published : 2021.11.30

Abstract

A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in 𝑙2(ℤN) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.

Keywords

References

  1. Z. Amiri, M. A. Dehghan, E. Rahimib & L. Soltania: Bessel subfusion sequences and subfusion frames. Iran. J. Math. Sci. Inform. 8 (2013), 31-38.
  2. P.G. Cazassa & G. Kutyniok: Frames of subspaces, wavelets, frames and operator theory. American Mathematical Society, Contemporary Mathematics Publishers 345 (2004), 87-113. https://doi.org/10.1090/conm/345/06242
  3. P.G. Cazassa & G. Kutyniok: Finite Frames Theory and Applications. Applied and Numerical Harmonic Analysis Series, Birkhauser, Boston, 2013.
  4. O. Christensen: An Introduction to Frames and Riesz Bases. Second Edition, Birkhauser, Boston, 2016.
  5. O. Christensen and Y.C. Eldar: Oblique dual frames and shift-invariant spaces. Appl. Comput. Harmon. Anal. 17 (2004), 48-68. https://doi.org/10.1016/j.acha.2003.12.003
  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. Schaeffler: A class of non-harmonic Fourier series. Trans. Amer. Math. Soc. 72 (1952), 341-366. https://doi.org/10.1090/S0002-9947-1952-0047179-6
  8. T.C. Easwaran Nambudiri & K. Parthasarathy: Generalised Weyl-Heisenberg frame operators. Bull. Sci. Math. 136 (2012), 44-53. https://doi.org/10.1016/j.bulsci.2011.09.001
  9. T.C. Easwaran Nambudiri & K. Parthasarathy: Characterization of Weyl-Heisenberg frame operators. Bull. Sci. Math. 137 (2013), 322-324. https://doi.org/10.1016/j.bulsci.2012.09.001
  10. D. Gabor: Theory of communication. Journal of Institution of Electrical Engineers 93 (1946), 429-457.
  11. K. Grochenig: Foundations of Time Frequency Analysis. Birkhauser, Boston, 2001.
  12. M. Janssen: Gabor representation of generalized functions. J. Math. Anal. Appl. 83 (1981), 377-394. https://doi.org/10.1016/0022-247x(81)90130-x
  13. J. Laurence: Linear independence of Gabor systems in finite dimensional vector spaces. J. Fourier Anal. Appl. 11 (2005), 715-726. https://doi.org/10.1007/s00041-005-5017-6
  14. S. Li & H. Ogawa: Pseudoframes for subspaces with applications. J. Fourier Anal. Appl. 10 (2004), 409-431. https://doi.org/10.1007/s00041-004-3039-0
  15. R.D. Malikiosis: A note on Gabor frames in finite dimensions. Appl. Comp. Harmonic Anal. 38 (2015), 318-330. https://doi.org/10.1016/j.acha.2014.06.004
  16. G.E. Pfander: Gabor frames in finite dimensions. Birkhauser, Boston, 2010.