Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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NATURAL ORTHONORMAL BASES ASSOCIATED WITH FINITE FRAMES

  • Received : 2006.10.12
  • Accepted : 2007.03.26
  • Published : 2007.03.25
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Abstract

In this paper we show that for each finite frame for a Hilbert space there are two orthonormal elements related to the optimal lower and upper bounds of the frame. Based on this we show that an orthonormal basis is naturally associated with every finite frame. We then analyze the relationship between such an orthonormal basis and the given finite frame.

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References

  1. P.G. Casazza, Characterizing Hilbert space frames with the subframe property, Illinois J. Math. 41 (1997), 648-666.
  2. P.G. Casazza and O. Christensen, Hilbert space frames containing a Riesz bais and Banach spaces which have no subspace isomorphic to co, J. Math. Anal. Appl. 202 (1996), 940-950. https://doi.org/10.1006/jmaa.1996.0355
  3. P.G. Casazza and O. Christensen, Frames containing a Riesz basis and preserva­tion of this property under perturbation, SIAM J. Math. Anal. 29 (1998), 266-278. https://doi.org/10.1137/S0036141095294250
  4. O. Christensen, Frame perturbations, Proc. Amer. Math. Soc. 123 (1995), 1217-1220. https://doi.org/10.1090/S0002-9939-1995-1231031-8
  5. O. Christensen, A Paley-Wiener theorem for frames, Proc. Amer. Soc. 123 (1995), 2199-2201. https://doi.org/10.1090/S0002-9939-1995-1246520-X
  6. O. Christensen, Frames containing a Riesz basis and approximation of the frame coefficients using finite dimensional methods, J. Math. Anal. Appl. 199 (1996), 256-270. https://doi.org/10.1006/jmaa.1996.0140
  7. O. Christensen, An introduction to frames and Riesz bases, Birkhauser, Boston, 2003.
  8. R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press, New York, 1980.