On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms
In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invarian...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-02-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/13/2/331 |
| _version_ | 1797396101809045504 |
|---|---|
| author | Junjian Zhao Marko Kostić Wei-Shih Du |
| author_facet | Junjian Zhao Marko Kostić Wei-Shih Du |
| author_sort | Junjian Zhao |
| collection | DOAJ |
| description | In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mover accent="true"><mi>p</mi><mo>→</mo></mover></msub><mrow><mo>(</mo><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula> are also given. |
| first_indexed | 2024-03-09T00:46:27Z |
| format | Article |
| id | doaj.art-292b6fdc1bce4bea9a24677adbd90ced |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T00:46:27Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-292b6fdc1bce4bea9a24677adbd90ced2023-12-11T17:28:52ZengMDPI AGSymmetry2073-89942021-02-0113233110.3390/sym13020331On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-NormsJunjian Zhao0Marko Kostić1Wei-Shih Du2School of Mathematical Sciences, Tiangong University, Tianjin 300387, ChinaFaculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, SerbiaDepartment of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, TaiwanIn this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>L</mi><mover accent="true"><mi>p</mi><mo>→</mo></mover></msub><mrow><mo>(</mo><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula> are also given.https://www.mdpi.com/2073-8994/13/2/331mixed-norm Lebesgue spacemixed-norm Wiener amalgam spaceshift-invariant subspacesampling theorystability theoryiterative algorithm |
| spellingShingle | Junjian Zhao Marko Kostić Wei-Shih Du On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms Symmetry mixed-norm Lebesgue space mixed-norm Wiener amalgam space shift-invariant subspace sampling theory stability theory iterative algorithm |
| title | On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms |
| title_full | On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms |
| title_fullStr | On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms |
| title_full_unstemmed | On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms |
| title_short | On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms |
| title_sort | on generalizations of sampling theorem and stability theorem in shift invariant subspaces of lebesgue and wiener amalgam spaces with mixed norms |
| topic | mixed-norm Lebesgue space mixed-norm Wiener amalgam space shift-invariant subspace sampling theory stability theory iterative algorithm |
| url | https://www.mdpi.com/2073-8994/13/2/331 |
| work_keys_str_mv | AT junjianzhao ongeneralizationsofsamplingtheoremandstabilitytheoreminshiftinvariantsubspacesoflebesgueandwieneramalgamspaceswithmixednorms AT markokostic ongeneralizationsofsamplingtheoremandstabilitytheoreminshiftinvariantsubspacesoflebesgueandwieneramalgamspaceswithmixednorms AT weishihdu ongeneralizationsofsamplingtheoremandstabilitytheoreminshiftinvariantsubspacesoflebesgueandwieneramalgamspaceswithmixednorms |