Asymptotics of orthogonal polynomial's entropy

被引：30

作者：

Aptekarev, A. I. ^{[1
]}

Dehesa, J. S. ^{[2
]}

Martinez-Finkelshtein, A. ^{[3
]}

机构：

[1] Russian Acad Sci, MV Keldysh Appl Math Inst, Moscow 125047, Russia

[2] Univ Granada, Inst Carlos Theoret & Computat Phys 1, E-18071 Granada, Spain

[3] Almeria Univ, Dept Appl Math & Stat, Almeria 04120, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 233卷 / 06期

关键词：

Information entropy; Uncertainty in quantum mechanics; Orthogonal polynomials; Asymptotics; Szego condition; Mutual energy; Logarithmic potential; INFORMATION ENTROPIES; BOUNDS;

D O I：

10.1016/j.cam.2009.02.056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This is a brief account on some results and methods of the asymptotic theory dealing with the entropy of orthogonal polynomials for large degree. This study is motivated primarily by quantum mechanics, where the wave functions and the densities of the states of solvable quantum-mechanical systems are expressed by means of orthogonal polynomials. Moreover, the uncertainty principle, lying in the ground of quantum mechanics, is best formulated by means of position and momentum entropies. In this sense, the behavior for large values of the degree is intimately connected with the information characteristics of high energy states. But the entropy functionals and their behavior have an independent interest for the theory of orthogonal polynomials. We describe some results obtained in the last 15 years, as well as sketch the ideas behind their proofs. (C) 2009 Elsevier B.V. All rights reserved,

引用

页码：1355 / 1365

页数：11

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