The Approximation Characteristics of Weighted <i>p</i>-Wiener Algebra
In this paper, we study the approximation characteristics of weighted <i>p</i>-Wiener algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script"...
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/18/3974 |
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| author | Ying Chen Xiangyu Pan Yanyan Xu Guanggui Chen |
| author_facet | Ying Chen Xiangyu Pan Yanyan Xu Guanggui Chen |
| author_sort | Ying Chen |
| collection | DOAJ |
| description | In this paper, we study the approximation characteristics of weighted <i>p</i>-Wiener algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script">A</mi><mrow><mi>ω</mi></mrow><mi>p</mi></msubsup><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula> defined on the <i>d</i>-dimensional torus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></semantics></math></inline-formula>. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mi>d</mi><mo>:</mo><msubsup><mi mathvariant="script">A</mi><mrow><mi>ω</mi></mrow><mi>p</mi></msubsup><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced><mo>→</mo><mi mathvariant="script">A</mi><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mi>d</mi><mo>:</mo><msubsup><mi mathvariant="script">A</mi><mrow><mi>ω</mi></mrow><mi>p</mi></msubsup><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced><mo>→</mo><msub><mi>L</mi><mi>q</mi></msub><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>p</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">A</mi><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced></mrow></semantics></math></inline-formula> is the Wiener algebra defined on the <i>d</i>-dimensional torus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T22:30:08Z |
| format | Article |
| id | doaj.art-8d6ec5fc8fa54345853fc7029f7fdebb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:30:08Z |
| publishDate | 2023-09-01 |
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| spelling | doaj.art-8d6ec5fc8fa54345853fc7029f7fdebb2023-11-19T11:50:10ZengMDPI AGMathematics2227-73902023-09-011118397410.3390/math11183974The Approximation Characteristics of Weighted <i>p</i>-Wiener AlgebraYing Chen0Xiangyu Pan1Yanyan Xu2Guanggui Chen3School of Science, Xihua University, Chengdu 610039, ChinaSchool of Science, Xihua University, Chengdu 610039, ChinaSchool of Science, Xihua University, Chengdu 610039, ChinaGraduate School, Xihua University, Chengdu 610039, ChinaIn this paper, we study the approximation characteristics of weighted <i>p</i>-Wiener algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script">A</mi><mrow><mi>ω</mi></mrow><mi>p</mi></msubsup><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula> defined on the <i>d</i>-dimensional torus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></semantics></math></inline-formula>. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mi>d</mi><mo>:</mo><msubsup><mi mathvariant="script">A</mi><mrow><mi>ω</mi></mrow><mi>p</mi></msubsup><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced><mo>→</mo><mi mathvariant="script">A</mi><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mi>d</mi><mo>:</mo><msubsup><mi mathvariant="script">A</mi><mrow><mi>ω</mi></mrow><mi>p</mi></msubsup><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced><mo>→</mo><msub><mi>L</mi><mi>q</mi></msub><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>p</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">A</mi><mfenced separators="" open="(" close=")"><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></mfenced></mrow></semantics></math></inline-formula> is the Wiener algebra defined on the <i>d</i>-dimensional torus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">T</mi><mi>d</mi></msup></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/11/18/3974Wiener algebraapproximation numbersKolmogorov numbersentropy numbers |
| spellingShingle | Ying Chen Xiangyu Pan Yanyan Xu Guanggui Chen The Approximation Characteristics of Weighted <i>p</i>-Wiener Algebra Mathematics Wiener algebra approximation numbers Kolmogorov numbers entropy numbers |
| title | The Approximation Characteristics of Weighted <i>p</i>-Wiener Algebra |
| title_full | The Approximation Characteristics of Weighted <i>p</i>-Wiener Algebra |
| title_fullStr | The Approximation Characteristics of Weighted <i>p</i>-Wiener Algebra |
| title_full_unstemmed | The Approximation Characteristics of Weighted <i>p</i>-Wiener Algebra |
| title_short | The Approximation Characteristics of Weighted <i>p</i>-Wiener Algebra |
| title_sort | approximation characteristics of weighted i p i wiener algebra |
| topic | Wiener algebra approximation numbers Kolmogorov numbers entropy numbers |
| url | https://www.mdpi.com/2227-7390/11/18/3974 |
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