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The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²)


Citation

Shamsah, Raghad Sahib and Ahatjonovich, Anvarjon Ahmedov and Zainuddin, Hishamuddin and Kilicman, Adem and Ismail, Fudziah (2017) The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²). International Journal of Pure and Applied Mathematics, 114 (3). pp. 523-536. ISSN 1311-8080; ESSN: 1314-3395

Abstract

We show that the two dimensional wavelet expansion of Lᴾ (R²) function for 1 < p < ∞ converges pointwise almost everywhere under wavelet projection operator. This convergence can be established by assuming some minimal regularity to get the rapidly decreasing for two dimensional wavelet ψj1,j2,k1,k2. The Kernel function of the wavelet projection operator in two dimension converges absolutely, distributionally and is bounded. Also the wavelet expansions in two dimension are controlled in a magnitude by the maximal function operator. All these conditions can be utilized to achieve the convergence almost everywhere.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.12732/ijpam.v114i3.9
Publisher: Academic Publications
Keywords: Two dimensional wavelet expansion; Kernel function; Almost everywhere convergence; Maximal function; Bounded
Depositing User: Nabilah Mustapa
Date Deposited: 04 Oct 2019 08:30
Last Modified: 04 Oct 2019 08:30
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.12732/ijpam.v114i3.9
URI: http://psasir.upm.edu.my/id/eprint/15567
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