hal-00015062, version 1
From asymptotics to spectral measures: determinate versus indeterminate moment problems
Mediterranean Journal of Mathematics, Vol. 3, pp. 327-345 (2006) (2006)
Abstract: 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.
- 1:
- CNRS : UMR7589 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
- 2:
- Université de la Méditerranée - Aix-Marseille II
- Domain : Physics/Mathematical Physics
- Keywords : Markov theorem – indeterminate moment problems – orthogonal polynomials
- Comment : Lecture given at the International Mediterranean Congress of Mathematics – Almeria – 6-10 june 2005.
- hal-00015062, version 1
- http://hal.archives-ouvertes.fr/hal-00015062
- oai:hal.archives-ouvertes.fr:hal-00015062
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- Submitted on: Friday, 2 December 2005 13:00:36
- Updated on: Monday, 2 October 2006 12:32:12
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