Smooth Molecular Decompositions of Functions and Singular Integral Operators

Released on by John E. Gilbert
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  • Smooth Molecular Decompositions of Functions and Singular Integral Operators Book Detail

  • Author : John E. Gilbert
  • Release Date : 2002
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 89
  • ISBN 13 : 0821827723
  • File Size : 47,47 MB
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Smooth Molecular Decompositions of Functions and Singular Integral Operators by John E. Gilbert PDF Summary

Book Description: Under minimal assumptions on a function $\psi$ the authors obtain wavelet-type frames of the form $\psi_{j, k}(x) = r DEGREES{(1/2)n j} \psi(r DEGREESj x - sk), j \in \integer, k \in \integer DEGREESn, $ for some $r > 1$ and $s > 0$. This collection is shown to be a frame for a scale of Triebel-Lizorkin spaces (which includes Lebesgue, Sobolev and Hardy spaces) and the reproducing formula converges in norm as well as pointwise a.e. The construction follows from a characterization of those operators which are bounded on a space of smooth molecules. This characterization also allows us to decompose a broad range of singular integral operators in ter

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Time‒Frequency and Time‒Scale Methods

Time‒Frequency and Time‒Scale Methods

File Size : 91,91 MB
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Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful