Abstract
In the Sobolev space \(W_p^k (\Omega )\), where Ω is a bounded domain in ℝn with a Lipschitzian boundary, for an arbitrarily given \(m \in \mathbb{N}\), we construct a basis such that the error of approximation of a function \(W_p^k (\Omega )\) the Nth partial sum of its expansion with respect to this basis can be estimated in terms of the modulus of smoothness \(\omega m(D^k f,N^{ - 1/n} )_{L_p (\Omega )} \) of order \(m\).
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Matveev, O.V. Bases in Sobolev Spaces on Bounded Domains with Lipschitzian Boundary. Mathematical Notes 72, 373–382 (2002). https://doi.org/10.1023/A:1020503505540
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DOI: https://doi.org/10.1023/A:1020503505540