Kolmogorov's problem on the class of multiply monotone functions

被引：1
|
作者：
Babenko, Vladyslav [1 ]
Babenko, Yuliya [2 ]
Kovalenko, Oleg [1 ,3 ]
机构：
[1] Dnepropetrovsk Natl Univ, Dept Math Anal & Theory Funct, UA-49050 Dnepropetrovsk, Ukraine
[2] Kennesaw State Univ, Dept Math, Kennesaw, GA 30144 USA
[3] Kennesaw State Univ, Kennesaw, GA 30144 USA
来源：
ADVANCES IN MATHEMATICS | 2015年 / 280卷
关键词：
Multiply monotone; Sharp inequalities; Derivatives; Kolmogorov's problem; Moment problem; Hermite-Birkhoff interpolation; Extremal problems; HERMITE-BIRKHOFF INTERPOLATION; EXTREMAL PROBLEMS; DERIVATIVES;
D O I：
10.1016/j.aim.2015.03.023
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we give necessary and sufficient conditions for the system of positive numbers M-k1, M-k2, ... , M-kd, 0 <= k(1) < ... < k(d) <= r, to guarantee the existence of an r-monotone function defined on the negative half-line R- and such that parallel to x((ki))parallel to(infinity) = M-ki, i = 1, 2, ... , d. We also discuss some applications of the obtained results and connections with other problems. (C) 2015 Elsevier Inc. All rights reserved.
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页码：256 / 281
页数：26
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