Extremal problems in nonquasianalytic Carleman classes. Applications

An extremal problem is considered in the family of functions in a nonquasianalytic Carleman class on a closed interval that vanish together with all derivatives at a point in this interval. Applications to approximation theory and, in particular, to a system of exponentials with exponents satisfying...

Full description

Saved in:
Bibliographic Details
Published in:Sbornik. Mathematics 2018-07, Vol.209 (7), p.958-984
Main Author: Gaisin, A. M.
Format: Article
Language:English
Subjects:
extremal problem
minimal system of exponentials
nonquasianalytic Carleman class
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An extremal problem is considered in the family of functions in a nonquasianalytic Carleman class on a closed interval that vanish together with all derivatives at a point in this interval. Applications to approximation theory and, in particular, to a system of exponentials with exponents satisfying the Fejér (or Levinson) condition are indicated; an asymptotic estimate as is obtained for the distance in between a fixed exponential and the closure of the linear span of other elements of this system. Bibliography: 25 titles.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM8758