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Asymptotics of orthogonal polynomial’s entropy

✍ Scribed by A.I. Aptekarev; J.S. Dehesa; A. Martinez-Finkelshtein

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
585 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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