| Autor: |
Kelly, S.E., Kon, M.A., Raphael, L.A. |
| Zdroj: |
Journal of Functional Analysis; November 15, 1994, Vol. 126 Issue: 1 p102-138, 37p |
| Abstrakt: |
Wavelets provide a new class of orthogonal expansions in L2(ℝd) with good time/frequency localization and regularity/approximation properties. They have been successfully applied to signal processing, numerical analysis, and quantum mechanics. We study pointwise convergence properties of wavelet expansions and show that such expansions (and more generally, multiscale expansions) of Lp functions (1 ≤ p ≤ ∞) converge pointwise almost everywhere, and more precisely everywhere on the Lebesgue set of the function being expanded. We show that such convergence is partially insensitive to the order of summation of the expansion. It is shown that unlike Fourier series, a wavelet expansion has a summation kernel which is absolutely bounded by dilations of a radial decreasing L1 convolution kernel H(|x − y|). This fact provides another proof of Lp convergence. These results hold in all dimensions, and apply to related multiscale expansions, including best approximations using spline functions.Copyright 1994, 1999 Academic Press, Inc. |
| Databáze: |
Supplemental Index |
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