Embeddings for infinite-dimensional integration and L_2-approximation with increasing smoothness

Gnewuch M.; Hefter M.; Hinrichs A.; Ritter K.; Wasilkowski G. W.

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Embeddings for infinite-dimensional integration and L_2-approximation with increasing smoothness

机译：光滑度不断提高的无穷维积分和L_2逼近的嵌入

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摘要

We study integration and L-2-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh, Haar, and Sobolev spaces. For the proofs we derive embedding theorems between spaces of increasing smoothness and appropriate weighted function spaces of fixed smoothness. (C) 2019 Elsevier Inc. All rights reserved.

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《Journal of complexity》 |2019年第10期|101406.1-101406.32|共32页
作者
Gnewuch M.; Hefter M.; Hinrichs A.; Ritter K.; Wasilkowski G. W.;
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作者单位

Christian Albrechts Univ Kiel, Math Seminar, Ludewig Meyn Str 4, D-24098 Kiel, Germany;

Tech Univ Kaiserslautern, Fachbereich Math, Postfach 3049, D-67653 Kaiserslautern, Germany;

Johannes Kepler Univ Linz, Inst Anal, Altenberger Str 69, A-4040 Linz, Austria;

Tech Univ Kaiserslautern, Fachbereich Math, Postfach 3049, D-67653 Kaiserslautern, Germany;

Univ Kentucky, Dept Comp Sci, Davis Marksbury Bldg,329 Rose St, Lexington, KY 40506 USA;

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正文语种 eng
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关键词
High-dimensional integration; Infinite-dimensional integration; Embedding theorems; Reproducing kernel Hilbert spaces; Tractability;

机译：高维集成;无限的一体化;嵌入定理;再现内核希尔伯特空间;遗传性;

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7. Embeddings for infinite-dimensional integration and L2-approximation with increasing smoothness [O] . M. Gnewuch, M. Hefter, A. Hinrichs, 2019

机译：嵌入无限尺寸集成和L2近似随着平滑性的增加

Embeddings for infinite-dimensional integration and L_2-approximation with increasing smoothness

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