The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²)
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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Academic Publications
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/15567/1/The%20point%20wise%20behavior%20of%202-dimensional%20wavelet%20expansions%20in%20L%E1%B4%BE%20R%C2%B2.pdf |
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| author | Shamsah, Raghad Sahib Ahatjonovich, Anvarjon Ahmedov Zainuddin, Hishamuddin Kilicman, Adem Ismail, Fudziah |
| author_facet | Shamsah, Raghad Sahib Ahatjonovich, Anvarjon Ahmedov Zainuddin, Hishamuddin Kilicman, Adem Ismail, Fudziah |
| author_sort | Shamsah, Raghad Sahib |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T07:34:43Z |
| format | Article |
| id | upm.eprints-15567 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:34:43Z |
| publishDate | 2017 |
| publisher | Academic Publications |
| record_format | dspace |
| spelling | upm.eprints-155672019-10-04T08:30:35Z http://psasir.upm.edu.my/id/eprint/15567/ The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²) Shamsah, Raghad Sahib Ahatjonovich, Anvarjon Ahmedov Zainuddin, Hishamuddin Kilicman, Adem Ismail, Fudziah 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. Academic Publications 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/15567/1/The%20point%20wise%20behavior%20of%202-dimensional%20wavelet%20expansions%20in%20L%E1%B4%BE%20R%C2%B2.pdf 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 https://ijpam.eu/contents/2017-114-3/9/index.html 10.12732/ijpam.v114i3.9 |
| spellingShingle | Shamsah, Raghad Sahib Ahatjonovich, Anvarjon Ahmedov Zainuddin, Hishamuddin Kilicman, Adem Ismail, Fudziah The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²) |
| title | The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²) |
| title_full | The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²) |
| title_fullStr | The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²) |
| title_full_unstemmed | The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²) |
| title_short | The point wise behavior of 2-dimensional wavelet expansions in Lᴾ (R²) |
| title_sort | point wise behavior of 2 dimensional wavelet expansions in lᴾ r² |
| url | http://psasir.upm.edu.my/id/eprint/15567/1/The%20point%20wise%20behavior%20of%202-dimensional%20wavelet%20expansions%20in%20L%E1%B4%BE%20R%C2%B2.pdf |
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