Titlebook: n-Widths in Approximation Theory; Allan Pinkus Book 1985 Springer-Verlag Berlin Heidelberg 1985 Approximation.analytic function.approximat

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Exact ,-Widths of Integral Operators,. is a nondegenerate totally positive kernel. (Such kernels were defined in Section 5 of Chapter IV and are redefined in Section 2.) We prove that all three .-widths considered are equal (the common value depending on . and .) and that there exists a set of . distinct points in {.}. in (0,1) for whi

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Asymptotic Estimates for ,-Widths of Sobolev Spaces,r of the values .(.;.), .(.; .) and ..(.;.) for .,., ∈[1, ∞] as . grows. It is only recently that this problem has been solved for all ., . ∈ [1, ∞] (and almost all .). We first state the major result proven in this chapter.

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-Widths of Analytic Functions,In this chapter we consider .-widths of various classes of analytic functions. Our concern is with exact .-widths and the identification of optimal subspaces. Asymptotic estimates are relegated to the “Notes and References” at the end of the chapter.

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