Best Approximation by Logarithmically Concave Classes of Functions

Dimiter Dryanov ()
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Dimiter Dryanov: Concordia University

A chapter in Progress in Approximation Theory and Applicable Complex Analysis, 2017, pp 317-339 from Springer

Abstract: Abstract The paper contains results on best approximation by logarithmically concave classes of functions. For example, we prove the following: Let 𝒫 c $$\mathcal{P}_{c}$$ denote the class of real polynomials, having − 1 and 1 as consecutive zeros, and whose zeros z k = x k +i y k , i 2 = −1, satisfy the inequality | y k | ≤ | x k | − 1. Let i(x) = 1, x ∈ [−1, 1] be the unit function on the interval [−1, 1] and 1 ≤ p

Keywords: Uniqueness of best approximation; Logarithmically concave classes of functions; Polynomials with only real zeros; Laguerre–Pólya class of entire functions; 41A30; 41A10; 41A50; 41A52 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-49242-1_15

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DOI: 10.1007/978-3-319-49242-1_15

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