The convergence of operator with rapidly decreasing wavelet functions
The expansion of (2D) wavelet functions with respect to Lp(R2) space converging almost everywhere for 1 < p < 1 throughout the length of the Lebesgue set points of space functions is investigated in this research. The convergence is established by assuming somewavelet function minimal regulari...
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia
2022
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| Online Access: | https://umpir.ump.edu.my/id/eprint/45349/ |
| _version_ | 1848827390960074752 |
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| author | Shamsah, Raghad S. Ahmedov, Anvarjon A. Kilicman, A. Zainuddin, H. |
| author_facet | Shamsah, Raghad S. Ahmedov, Anvarjon A. Kilicman, A. Zainuddin, H. |
| author_sort | Shamsah, Raghad S. |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | The expansion of (2D) wavelet functions with respect to Lp(R2) space converging almost everywhere for 1 < p < 1 throughout the length of the Lebesgue set points of space functions is investigated in this research. The convergence is established by assuming somewavelet function minimal regularity ψ j1;j2;k1;k2 under the current description of the wavelet projection operator known as 2D Hard Sampling Operator. Note that the feature of fast decline in 2D is derived here. Another condition is used, for instance, the wavelet expansion’s boundedness under the Hard Sampling Operator. The bound (limit) is governed in magnitude with respect to the maximal equality of the Hardy-Littlewood maximal operator. Some ideas presented in this work to find a new method to prove the convergence theory for new type of conditional wavelet operator. Propose some conditions for wavelets functions and there expansion can support the operator to be convergence. It also perform a comparison with the identity convergent operator is our method for achieving this convergence. |
| first_indexed | 2025-11-15T03:59:58Z |
| format | Article |
| id | ump-45349 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T03:59:58Z |
| publishDate | 2022 |
| publisher | Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-453492025-08-12T01:18:37Z https://umpir.ump.edu.my/id/eprint/45349/ The convergence of operator with rapidly decreasing wavelet functions Shamsah, Raghad S. Ahmedov, Anvarjon A. Kilicman, A. Zainuddin, H. QA Mathematics T Technology (General) The expansion of (2D) wavelet functions with respect to Lp(R2) space converging almost everywhere for 1 < p < 1 throughout the length of the Lebesgue set points of space functions is investigated in this research. The convergence is established by assuming somewavelet function minimal regularity ψ j1;j2;k1;k2 under the current description of the wavelet projection operator known as 2D Hard Sampling Operator. Note that the feature of fast decline in 2D is derived here. Another condition is used, for instance, the wavelet expansion’s boundedness under the Hard Sampling Operator. The bound (limit) is governed in magnitude with respect to the maximal equality of the Hardy-Littlewood maximal operator. Some ideas presented in this work to find a new method to prove the convergence theory for new type of conditional wavelet operator. Propose some conditions for wavelets functions and there expansion can support the operator to be convergence. It also perform a comparison with the identity convergent operator is our method for achieving this convergence. Universiti Putra Malaysia 2022 Article PeerReviewed pdf en https://umpir.ump.edu.my/id/eprint/45349/1/The%20convergence%20of%20operator%20with%20rapidly%20decreasing%20wavelet%20functions.pdf Shamsah, Raghad S. and Ahmedov, Anvarjon A. and Kilicman, A. and Zainuddin, H. (2022) The convergence of operator with rapidly decreasing wavelet functions. Malaysian Journal of Mathematical Sciences, 16 (4). pp. 683-695. ISSN 1823-8343 (Print); 2289-750X (Online). (Published) https://doi.org/10.47836/mjms.16.4.03 https://doi.org/10.47836/mjms.16.4.03 https://doi.org/10.47836/mjms.16.4.03 |
| spellingShingle | QA Mathematics T Technology (General) Shamsah, Raghad S. Ahmedov, Anvarjon A. Kilicman, A. Zainuddin, H. The convergence of operator with rapidly decreasing wavelet functions |
| title | The convergence of operator with rapidly decreasing wavelet functions |
| title_full | The convergence of operator with rapidly decreasing wavelet functions |
| title_fullStr | The convergence of operator with rapidly decreasing wavelet functions |
| title_full_unstemmed | The convergence of operator with rapidly decreasing wavelet functions |
| title_short | The convergence of operator with rapidly decreasing wavelet functions |
| title_sort | convergence of operator with rapidly decreasing wavelet functions |
| topic | QA Mathematics T Technology (General) |
| url | https://umpir.ump.edu.my/id/eprint/45349/ https://umpir.ump.edu.my/id/eprint/45349/ https://umpir.ump.edu.my/id/eprint/45349/ |