The Approximation Characteristics of Weighted <i>p</i>-Wiener Algebra

• 出版年: Mathematics
• 主要な著者: Ying Chen, Xiangyu Pan, Yanyan Xu, Guanggui Chen
• フォーマット: 論文
• 言語: 英語
• 出版事項: MDPI AG 2023-09-01
• 主題: Wiener algebra; approximation numbers; Kolmogorov numbers; entropy numbers
• オンライン･アクセス: https://www.mdpi.com/2227-7390/11/18/3974

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>.