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ON STABILITY OF BANACH FRAMES

  • Published : 2007.02.28

Abstract

Some stability theorems (Paley-Wiener type) for Banach frames in Banach spaces have been derived.

Keywords

References

  1. R. Balan, Stability theorems for Fourier frames and wavelet Riesz bases, J. Fourier Anal. Appl. 3 (1997), no. 5, 499-504 https://doi.org/10.1007/BF02648880
  2. P. G. Casazza, D. Han, and D. R. Larson, Frames for Banach spaces, Contem. Math. 247 (1999), 149-182 https://doi.org/10.1090/conm/247/03801
  3. O. Christensen, A Paley-Wiener Theorem for frames, Proc. Amer. Math. Soc. 123 (1995), no. 7, 2199-2201
  4. O. Christensen and C. Heil, Perturbations of Banach frames and atomic decompositions, Math. Nachr. 185 (1997), 33-47 https://doi.org/10.1002/mana.3211850104
  5. R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569-645 https://doi.org/10.1090/S0002-9904-1977-14325-5
  6. I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 27 (1986), no. 5, 1271-1283 https://doi.org/10.1063/1.527388
  7. R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341-366. https://doi.org/10.2307/1990760
  8. S. J. Favier and R. A. Zalik, On the stability of frames and Riesz bases, Appl. Comput. Harmon. Anal. 2 (1995), no. 2, 160-173. https://doi.org/10.1006/acha.1995.1012
  9. H. G. Feichtinger and K. Grochenig, A unified approach to atomic decompositions via integrable group representations, In: Proc. Conf. 'Function Spaces and Applications', Lecture Notes Math. 1302, Berling - Heidelberg - New York: Springer (1988), 52-73 https://doi.org/10.1007/BFb0078857
  10. K. Grochenig, Describing functions: Atomic decompositions versus frames, Monatsh. Math. 112 (1991), no. 1, 1-41 https://doi.org/10.1007/BF01321715
  11. I. Singer, Bases in Banach space-II, Springer Verlag, 1981
  12. J. Zhang, Stability of wavelet frames and Riesz bases, with respect to dilations and translations, Proc. Amer. Math. Soc. 129 (2001), no. 4, 1113-1121 https://doi.org/10.1090/S0002-9939-00-05660-4

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