A+ CATEGORY SCIENTIFIC UNIT

Unconditional biorthogonal wavelet bases in $L^p({\Bbb R}^d)$

Volume 92 / 2002

Waldemar Pompe Colloquium Mathematicum 92 (2002), 19-34 MSC: 42C10, 46B15, 46E30. DOI: 10.4064/cm92-1-2

Abstract

We prove that a biorthogonal wavelet basis yields an unconditional basis in all spaces $L^{p}({\mathbb R}^d)$ with $1< p< \infty $, provided the biorthogonal wavelet set functions satisfy weak decay conditions. The biorthogonal wavelet set is associated with an arbitrary dilation matrix in any dimension.

Authors

  • Waldemar PompeFB Mathematik, AG6
    Schloßgartenstr. 7
    64289 Darmstadt, Germany
    e-mail

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