The truncated moment problem on N0

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Infusino, M.¹  Kuna, T.²  Lebowitz, J. L.^3,4  Speer, E. R.³ 

[1] Univ Konstanz, Dept Math & Stat, Univ Str 10, D-78457 Constance, Germany

[2] Univ Reading, Dept Math & Stat, POB 220, Reading RG6 6AX, Berks, England

[3] Rutgers State Univ, Dept Math, New Brunswick, NJ 08903 USA

[4] Rutgers, Dept Phys, New Brunswick, NJ USA

关键词: Truncated moment problem;    Discrete moment problem;    Realizability;   

DOI  :  10.1016/j.jmaa.2017.02.060

来源: Elsevier

【 摘 要 】

We find necessary and sufficient conditions for the existence of a probability measure on N-0, the nonnegative integers, whose first n moments are a given n-tuple of nonnegative real numbers. The results, based on finding an optimal polynomial of degree n which is nonnegative on N-0 (and which depends on the moments), and requiring that its expectation be nonnegative, generalize previous results known for n = 1, n = 2 (the Percus Yamada condition), and partially for n = 3. The conditions for realizability are given explicitly for n <= 5 and in a finitely computable form for n >= 6. We also find, for all n, explicit bounds, in terms of the moments, whose satisfaction is enough to guarantee realizability. Analogous results are given for the truncated moment problem on an infinite discrete semi-bounded subset of R. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free