THE STABILITY OF HILBERT SPACE FRAMELETS AND RIESZ FRAMES

  • LEE, JEONG-GON (Department of Mathematics Won Kwang University) ;
  • LEE, DONG-MYUNG (Department of Mathematics Won Kwang University)
  • Received : 2005.08.04
  • Accepted : 2005.10.25
  • Published : 2005.12.25

Abstract

We consider the stability of Hilbert space framelets and related Riesz frames. Our results are in spirit close to classical results for orthonormal bases, due to Mazur and Schauder.

Keywords

Acknowledgement

Supported by : Won Kwang University

References

  1. J. of Math. Anal. and Appl. v.202 Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$ Casazza, P.G.;Christensen, O.
  2. Illinois J. Math. v.43 no.2 Local theory of frames and Schauder bases for Hilbert spaces Casazza, P.G.
  3. Appl. Comp. Harm. Anal v.1 Frames and the Projection Method Christensen, O.
  4. Proc. Amer. Math. Soc. v.123 no.4 Frame Perturbations Christensen, O.
  5. J. Math. Anal. Appl. v.199 Frames containing a Riesz basis and approximation of the frame coefficients using finite-dimensional methods Christensen, O.
  6. Appl. Comp. Harm. Anal. v.1 Bessel sequences and affine frames Chui, C.K.;Shi, X.
  7. Fourier Transforms and Wavelet Analysis Cui, M.G.;Lee, D.M.;Lee, J.G.
  8. Appl. Comput. Harmon. Anal. v.14 Framelets : MRA-based constructions of wavelet frames Daubechies, I.;Han, B.;Ron, A.;Shen, Z.W.
  9. Appl. Comput. Harmon. Anal. v.124 Framelets : MRA-based constructions of wavelet frames Daubechies, I.;Han, B.;Ron, A.;Shen, Z.W.
  10. Sequences and Series in Banach spaces Diestel, J.
  11. Memoris Amer. Math. Soc. v.147 Frames, bases, and group representations Han, S.;Larson, D.R.
  12. Appl. Comp. Harm. Anal. v.4 New characterizations of Riesz bases Kim, H.O.;Lim, J.K.
  13. Topological vector spaces II Kothe, G.
  14. Far East J. Math. Sci. v.3 no.5 Stability of quasiftames with quasiframe operators Lee, J.G.;Kim, I.K.;Lee, D.M.
  15. J. Korea Soc. Math. Educ. Ser. B: pure Appl. Math. v.11 no.2 Representation of solutions of Fredholm equations in $W^{2}_{2}({\Omega})$ of reproducing kernels Lee, D.M.;Lee, J.G.;Cui, M.G.
  16. Appl. Comput. Harmon. Analysis v.11 no.2 Explicit Construction of framelets Petukhov, A.
  17. An Introduction to Nonharmonic Fourier Series Young, R.M.