On certain extremal problems
type: Item
instance of: scholarly article
title: On certain extremal problems
zbMATH Open document ID: 0612.42012
author: H. S. Cocharyan
author: V. M. Martirosyan
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The following problem is considered: given a linearly independent system \(\{x_ j\}^ n_ 1\) in a Hilbert space, find the largest value of \(\max_{1\leq k\leq n}| d_ k|\) under the condition that \(\| d_ 1x_ 1+...+d_ nx_ n\| \leq 1\). For certain classical systems of rational fractions, exponentials, etc. the authors find this largest value and give explicit formulae for the extremal 'polynomial' \(d_ 1x_ 1+...+d_ nx_ n\). (For example, the system \(\{(\exp (-\lambda_ jt))t^{s_ j-1}\}\quad 1\leq j\leq n\) in \(L^ 2({\mathbb{R}}_+)\) is considered, where Re\(\lambda_ j>0\) and \(s_ k=card \{i\leq k:\lambda_ i=\lambda_ k\}.)\)
Mathematics Subject Classification ID: 42C99
zbMATH DE Number: 3990046
zbMATH Keywords: extremal polynomial
zbMATH Keywords: Hilbert space
reviewed by: S. V. Kislyakov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3990046