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Dyadic Localization

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1767)

Abstract

This chapter contains a local analysis of Q p(T) based on the dyadic portions. First of all, we give an alternate characterization of Q p in terms of the square mean oscillations over successive bipartitions of arcs in T. Next, we consider the dyadic counterpart Q p d(T) of Q p(T), in particular, we show that fQ p(T) if and only if (almost) all its translates belong to Q d p(T); conversely, functions in Q p(T) may be obtained by averaging translates of functions in Q p(T). Finally, as a natural application of the dyadic model of Q p(T), we present a wavelet expansion theorem of Q p(T).

Keywords

  • Wavelet Coefficient
  • Dyadic Interval
  • Haar System
  • Haar Function
  • Complete Orthonormal Basis

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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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). Dyadic Localization. In: Xiao, J. (eds) Holomorphic Q Classes. Lecture Notes in Mathematics, vol 1767. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45434-9_8

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  • DOI: https://doi.org/10.1007/3-540-45434-9_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42625-7

  • Online ISBN: 978-3-540-45434-2

  • eBook Packages: Springer Book Archive