RELATIVE WIDTH OF SMOOTH CLASSES OF MULTIVARIATE PERIODIC FUNCTIONS WITH RESTRICTIONS ON ITERATED LAPLACE DERIVATIVES IN THE L2-METRIC |
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| Authors: | Yongping Liu Lianhong Yang |
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| Institution: | aSchool of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;bDepartment of Applied Mathematics, Communication University of China, Beijing 100024, China |
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| Abstract: | For two subsets W and V of a Banach space X, let Kn (W, V, X) denote the relative Kolmogorov n-width of W relative to V defined by where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2(Δr) denote the class of 2π-periodic functions f with d-variables satisfying | while Δr is the r-iterate of Laplace operator Δ. This article discusses the relative Kolmogorov n-width of W2(Δr) relative to W2(Δr) in Lq (−π, π]d) (1 ≤ q ≤ ∞), and obtain its weak asymptotic result.
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| Keywords: | Multivariate function classes width relative width |
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