From asymptotics to spectral measures: determinate versus indeterminate moment problems

Details From asymptotics to spectral measures: determinate versus indeterminate moment problems From asymptotics to spectral measures: determinate versus indeterminate moment problems

2005-12-02

arxiv.org/abs/math-ph/0512005v1

International Mediterranean Congress of Mathematics, Almeria, 6-10 june 2005, Espagne (2006) 327-345

Physics

Mathematical Physics

Lecture given at the International Mediterranean Congress of Mathematics, Almeria, 6-10 june 2005, latex2e, 16 pages

Scientific paper

10.1007/s00009-006-0068-8

In the field of orthogonal polynomials theory, the classical Markov theorem shows that for determinate moment problems the spectral measure is under control of the polynomials asymptotics. The situation is completely different for indeterminate moment problems, in which case the interesting spectral measures are to be constructed using Nevanlinna theory. Nevertheless it is interesting to observe that some spectral measures can still be obtained from weaker forms of Markov theorem. The exposition will be illustrated by orthogonal polynomials related to elliptic functions: in the determinate case by examples due to Stieltjes and some of their generalizations and in the indeterminate case by more recent examples.

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