2013/03/02 by I. V. Boykov, Boykov, Ilya V. · 1 citation
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #Numerical methods in inverse problems #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1303.0416
openalex publication_date 2013/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Solutions of numerous equations of mathematical physics such as elliptic,\nweakly singular, singular, hypersingular integral equations belong to\nfunctional classes Qur \γ(\Ω,1) and Qur\n\γ(\Ω,1) defined over l-dimensional hypercube \Ω=[-1,1]l,\nl=1,2,.... The derivatives of classes' representatives grow indefinitely when\nthe argument approaches the boundary \δ \Ω. In this paper we estimate\nthe Kolmogorov and Babenko widths of two functional classes Qur\n\γ(\Ω,1) and Qur \γ(\Ω,1). We construct local splines\nbelonging to those classes, such that the errors of approximation are of the\nsame order as that of the estimated widths. Thus we construct optimal with\nrespect to order methods for approximating the functional classes Qur\n\γ(\Ω,1) and Qur \γ(\Ω,1). One can use these results\nfor constructing methods optimal with respect to order for approximating a unit\nball of the Sobolev spaces with logarithmic and polynomial weights.\n