A+ CATEGORY SCIENTIFIC UNIT

Haar wavelets on the Lebesgue spaces of local fields of positive characteristic

Volume 136 / 2014

Biswaranjan Behera Colloquium Mathematicum 136 (2014), 149-168 MSC: Primary 42C40; Secondary 42C15, 43A70, 11S85. DOI: 10.4064/cm136-2-1

Abstract

We construct the Haar wavelets on a local field $K$ of positive characteristic and show that the Haar wavelet system forms an unconditional basis for $L^p(K)$, $1< p< \infty $. We also prove that this system, normalized in $L^p(K)$, is a democratic basis of $L^p(K)$. This also proves that the Haar system is a greedy basis of $L^p(K)$ for $1< p< \infty $.

Authors

  • Biswaranjan BeheraStatistics and Mathematics Unit
    Indian Statistical Institute
    203 B. T. Road
    Kolkata, 700108, India
    e-mail

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