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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Official URL or Download Paper: https://ijpam.eu/contents/2017-114-3/9/index.html
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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 |
| Statistic Details: | View Download Statistic |
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