Optimal approximation of multivariate periodic Sobolev functions in the sup-norm

2015/05/11 by Fernando Cobos, Thomas Kühn, Cobos, Fernando +3
Mathematics · #41A25 #46E35 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #math.FA #msc:41A25 #msc:46E35

paper · pdf · doi:10.48550/arxiv.1505.02636

arxiv created 2015/05/11 · openalex publication_date 2015/05/11 · arxiv updated 2015/05/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Using tools from the theory of operator ideals and s-numbers, we develop a general approach to transfer estimates for L₂ -approximation of Sobolev functions into estimates for L_∞-approximation, with precise control of all involved constants. As an illustration, we derive some results for periodic isotropic Sobolev spaces H^s (\mathbb T^d) and Sobolev spaces of dominating mixed smoothness H^s_{\rm mix} (\mathbb T^d), always equipped with natural norms. Some results for isotropic as well as dominating mixed Besov spaces are also obtained.

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