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Nonlinear Wavelet Approximation in the Space C(Rd)

  • Ronald A. DeVore
  • Pencho Petrushev
  • Xiang Ming Yu
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 19)

Abstract

We discuss the nonlinear approximation of functions from the space C(R d ) by a linear combination of n translated dilates of a fixed function ϕ.

Keywords

Besov Space Wavelet Decomposition Nonlinear Approximation Orthogonal Wavelet Dyadic Cube 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    C. de Boor and R.Q. Jia, Controlled approximation and a characterization of the local approximation order, Proc. Amer. Math. Soc. 95(1985), 547–553.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    A. Caveretta, W. Dahmen, and C. Micchelli, Stationary Subdivision, preprint.Google Scholar
  3. [3]
    I. Daubechies, Orthonormal basis of compactly supported wavelets, Communications on Pure & Applied Math. 41(1988), 909–996.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    R. DeVore, B. Jawerth, and Brad Lucier, Surface compression, preprint.Google Scholar
  5. [5]
    R. DeVore, B. Jawerth, and Brad Lucier, Image compression through transform coding, preprint.Google Scholar
  6. [6]
    R. DeVore, B. Jawerth, and V. Popov Compression of wavelet decompositions, preprint.Google Scholar
  7. [7]
    R. DeVore and V. Popov, Free multivariate splines, Constr. Approx. 3(1987), 239–248.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    R. DeVore and V. Popov Interpolation spaces and nonlinear approximation, In: Functions Spaces and Approximation, (Eds.: M. Cwikel, J. Peetre, Y. Sagher, H. Wallin), Vol. 1302, 1986, Springer Lecture Notes in Math (1988), 191–207.CrossRefGoogle Scholar
  9. [9]
    M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Math. J., 34(1985), 777–799.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, to appear in J. of Functional Analysis; also in MSRJ reports 00321-89, 00421-89 (1988).Google Scholar
  11. [11]
    Y. Meyer, Ondelletes et Opérateurs, Hermann Publ., France, 1990.Google Scholar
  12. [12]
    P. Petrushev, Direct and converse theorems for spline and rational approximation and Besov spaces, In: Functions Spaces and Approximation, (Eds.: M. Cwikel, J. Peetre, Y. Sagher, H. Wallin), Springer Lecture Notes in Math, Vol. 1302, 1986, pp. 363–377.CrossRefGoogle Scholar
  13. [13]
    V. Peller, Hankel operators of the class (PROPORTIONAL)p and their applications (Rational approximation, Gaussian processes, majorant problem for operators), Math. USSR-Sb., 122(1980), 538–581.MathSciNetGoogle Scholar
  14. [14]
    I.J Schoenberg, Cardinal Spline Interpolation, SIAM CBMS 12 (1973).zbMATHGoogle Scholar
  15. [15]
    G. Strang and G.F. Fix, A Fourier analysis of the finite element method, In: Constructive Aspects of Functional Analysis, G. Geymonant, ed., C.I.M.E. II Cilo, 1971, pp. 793–840.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Ronald A. DeVore
    • 1
  • Pencho Petrushev
    • 2
  • Xiang Ming Yu
    • 3
  1. 1.Deptartment of MathematicsUniv. of South CarolinaColumbiaUSA
  2. 2.Mathematics InstituteBulgarian Academy of SciencesBulgaria
  3. 3.Department of MathematicsSouthwest Missouri State UniversitySpringfieldUSA

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