From Asymptotics to Spectral Measures: Determinate Versus Indeterminate Moment Problems |
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Authors: | Galliano Valent |
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Institution: | (1) Laboratoire de Physique Théorique et des Hautes Energies, CNRS, Unité associée URA 280, 2 Place Jussieu, F-75251 Paris Cedex 05, France;(2) Present address: Département de Mathématiques, UFR Sciences-Luminy, Case 901, 163 Avenue de Luminy, 13258 Marseille Cedex 9, France |
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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 parametrization. Nevertheless it is interesting to observe that some spectral measures
can still be obtained from weaker forms of the 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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Keywords: | Primary 33C45 30B70 39A10 Secondary 44A60 33E05 |
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