Nonlinear Wavelet Approximation in the Space C(Rd)

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


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.


Besov Space Wavelet Decomposition Nonlinear Approximation Orthogonal Wavelet Dyadic Cube 
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  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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