@article{Ding2025, 
author = {Weiran Ding and Jiansong Li and Yumeng Jia and Wanru Yang},
title = {Tractability of        L    2  -approximation and integration over weighted Korobov spaces of increasing smoothness in the worst case setting},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {2},
pages = {1160-1184},
keywords = {L2-approximation, integration, tractability, Korobov space, increasing smoothness},
url = {https://www.sciopen.com/article/10.3934/era.2025052},
doi = {10.3934/era.2025052},
abstract = {This paper is devoted to the study of tractability of the        L    2  -approximation and integration from weighted Korobov spaces of increasing smoothness in the worst-case setting. The considered algorithms use information from the class        Λ          a      l      l      , including all continuous linear functionals, and from the class        Λ          s      t      d      , including function evaluations. Necessary and sufficient conditions on the weights of the function space for strong polynomial tractability, polynomial tractability, quasi-polynomial tractability, uniform weak tractability, weak tractability and    (  σ  ,  τ  )-weak tractability, are provided. Our results give a comprehensive picture of the weight conditions for all standard notions of algebraic tractability. It may be helpful to study the tractability of nonhomogeneous tensor product spaces.}
}