The Approximation Characteristics of Weighted p-Wiener Algebra

Chen, Ying; Pan, Xiangyu; Xu, Yanyan; Chen, Guanggui

doi:10.3390/math11183974

Open AccessArticle

The Approximation Characteristics of Weighted p-Wiener Algebra

¹

School of Science, Xihua University, Chengdu 610039, China

²

Graduate School, Xihua University, Chengdu 610039, China

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2023, 11(18), 3974; https://doi.org/10.3390/math11183974

Submission received: 14 August 2023 / Revised: 10 September 2023 / Accepted: 15 September 2023 / Published: 19 September 2023

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Abstract

In this paper, we study the approximation characteristics of weighted p-Wiener algebra

A_{ω}^{p} (T^{d})

for

1 \leq p < \infty

defined on the d-dimensional torus

T^{d}

. In particular, we investigate the asymptotic behavior of the approximation numbers, Kolmogorov numbers, and entropy numbers associated with the embeddings

i d : A_{ω}^{p} (T^{d}) \to A (T^{d})

and

i d : A_{ω}^{p} (T^{d}) \to L_{q} (T^{d})

for

1 \leq p

,

q < \infty

, where

A (T^{d})

is the Wiener algebra defined on the d-dimensional torus

T^{d}

.

Keywords: Wiener algebra; approximation numbers; Kolmogorov numbers; entropy numbers

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MDPI and ACS Style

Chen, Y.; Pan, X.; Xu, Y.; Chen, G. The Approximation Characteristics of Weighted p-Wiener Algebra. Mathematics 2023, 11, 3974. https://doi.org/10.3390/math11183974

AMA Style

Chen Y, Pan X, Xu Y, Chen G. The Approximation Characteristics of Weighted p-Wiener Algebra. Mathematics. 2023; 11(18):3974. https://doi.org/10.3390/math11183974

Chicago/Turabian Style

Chen, Ying, Xiangyu Pan, Yanyan Xu, and Guanggui Chen. 2023. "The Approximation Characteristics of Weighted p-Wiener Algebra" Mathematics 11, no. 18: 3974. https://doi.org/10.3390/math11183974

APA Style

Chen, Y., Pan, X., Xu, Y., & Chen, G. (2023). The Approximation Characteristics of Weighted p-Wiener Algebra. Mathematics, 11(18), 3974. https://doi.org/10.3390/math11183974

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