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Constructive Approximation

, Volume 8, Issue 2, pp 211–222 | Cite as

Geometrical dimension versus smoothness

  • Anca Deliu
  • Björn Jawerth
Article

Abstract

We study the relation between geometric dimension and smoothness, and give a precise characterization of the fractal dimension of the graph of a function in terms of smoothness classes of functions. We also express the fractal dimension in terms of different classical oscillation measures and in terms of wavelet expansions.

AMS classification

Primary 46E35 Secondary 58F11 

Key words and phrases

Fractal dimension Wavelets Besov space Smoothness space 

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Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • Anca Deliu
    • 1
  • Björn Jawerth
    • 2
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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