Embeddings for infinite-dimensional integration and L2-approximation with increasing smoothness

Michael Gwenuch; Mario Hefter; Aicke Hinrichs; Klaus Ritter; G.W. Wasilkowski

doi:10.1016/j.jco.2019.04.002

Embeddings for infinite-dimensional integration and L2-approximation with increasing smoothness

Michael Gwenuch, Mario Hefter, Aicke Hinrichs, Klaus Ritter, G.W. Wasilkowski

Department of Functional Analysis

Research output: Contribution to journal › Article › peer-review

Abstract

We study integration and L2-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.

Original language	English
Article number	101406
Number of pages	32
Journal	Journal of Complexity
Volume	54
DOIs	https://doi.org/10.1016/j.jco.2019.04.002
Publication status	Published - 2019

Fields of science

101002 Analysis
101032 Functional analysis

JKU Focus areas

Digital Transformation

Access to Document

10.1016/j.jco.2019.04.002

Cite this

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title = "Embeddings for infinite-dimensional integration and L2-approximation with increasing smoothness",

abstract = "We study integration and L2-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.",

author = "Michael Gwenuch and Mario Hefter and Aicke Hinrichs and Klaus Ritter and G.W. Wasilkowski",

year = "2019",

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AU - Gwenuch, Michael

AU - Hefter, Mario

AU - Hinrichs, Aicke

AU - Ritter, Klaus

AU - Wasilkowski, G.W.

PY - 2019

Y1 - 2019

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AB - We study integration and L2-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.

U2 - 10.1016/j.jco.2019.04.002

DO - 10.1016/j.jco.2019.04.002

M3 - Article

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VL - 54

JO - Journal of Complexity

JF - Journal of Complexity

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ER -