A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev Spaces
In recent years, dual wavelet frames derived from a pair of refinable functions have been widely studied by many researchers. However, the requirement of the Bessel property of wavelet systems is always required, which is too technical and artificial. In present paper, we will relax this restriction...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/1372184 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567911903920128 |
|---|---|
| author | Jianping Zhang |
| author_facet | Jianping Zhang |
| author_sort | Jianping Zhang |
| collection | DOAJ |
| description | In recent years, dual wavelet frames derived from a pair of refinable functions have been widely studied by many researchers. However, the requirement of the Bessel property of wavelet systems is always required, which is too technical and artificial. In present paper, we will relax this restriction and only require the integer translation of the wavelet functions (or refinable functions) to form Bessel sequences. For this purpose, we introduce the notion of weak dual wavelet frames. And for generality, we work under the setting of reducing subspaces of Sobolev spaces, we characterize a pair of weak dual wavelet frames, and by using this characterization, we obtain a mixed oblique extension principle for such weak dual wavelet frames. |
| format | Article |
| id | doaj-art-03ecd159b99d4b588630f8f998004484 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-03ecd159b99d4b588630f8f9980044842025-02-03T01:00:13ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/1372184A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev SpacesJianping Zhang0College of Mathematics and Computer ScienceIn recent years, dual wavelet frames derived from a pair of refinable functions have been widely studied by many researchers. However, the requirement of the Bessel property of wavelet systems is always required, which is too technical and artificial. In present paper, we will relax this restriction and only require the integer translation of the wavelet functions (or refinable functions) to form Bessel sequences. For this purpose, we introduce the notion of weak dual wavelet frames. And for generality, we work under the setting of reducing subspaces of Sobolev spaces, we characterize a pair of weak dual wavelet frames, and by using this characterization, we obtain a mixed oblique extension principle for such weak dual wavelet frames.http://dx.doi.org/10.1155/2022/1372184 |
| spellingShingle | Jianping Zhang A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev Spaces Journal of Function Spaces |
| title | A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev Spaces |
| title_full | A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev Spaces |
| title_fullStr | A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev Spaces |
| title_full_unstemmed | A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev Spaces |
| title_short | A Class of Weak Dual Wavelet Frames for Reducing Subspaces of Sobolev Spaces |
| title_sort | class of weak dual wavelet frames for reducing subspaces of sobolev spaces |
| url | http://dx.doi.org/10.1155/2022/1372184 |
| work_keys_str_mv | AT jianpingzhang aclassofweakdualwaveletframesforreducingsubspacesofsobolevspaces AT jianpingzhang classofweakdualwaveletframesforreducingsubspacesofsobolevspaces |