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

Biswaranjan Behera

Colloquium Mathematicae, Tome 135 (2014), p. 149-168 / Harvested from The Polish Digital Mathematics Library

Résumé

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 < ∞. 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 < ∞.

Publié le : 2014-01-01

Zbl 1304.42083

EUDML-ID : urn:eudml:doc:283665

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     title = {Haar wavelets on the Lebesgue spaces of local fields of positive characteristic},
     journal = {Colloquium Mathematicae},
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     year = {2014},
     pages = {149-168},
     zbl = {1304.42083},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-2-1}
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Biswaranjan Behera. Haar wavelets on the Lebesgue spaces of local fields of positive characteristic. Colloquium Mathematicae, Tome 135 (2014) pp. 149-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-2-1/