On some indeterminate moment problems for measures on a geometric progression (Q1298551)
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scientific article; zbMATH DE number 1326357
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some indeterminate moment problems for measures on a geometric progression |
scientific article; zbMATH DE number 1326357 |
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On some indeterminate moment problems for measures on a geometric progression (English)
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25 January 2000
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Some indeterminate moment problems with discrete measures are considered. Especially,the author studies solutions of these problems, which are associated with the discrete \(q\)-Hermite polynomials II, with the Stieltjes-Wigert polynomials in the case of log-normal distribution, and finally the same treatment is done for the \(q\)-Laguerre polynomials. These problems have a discrete solution concentrated on a geometric progression. It is possible that the number of solutions is infinite. Such questions are motivated by the study of a \(q\)-deformation of the harmonic oscillator.
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\(q\)-orthogonal polynomials
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\(q\)-Hermite polynomials II
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\(q\)-Laguerre polynomials
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\(q\)-deformation
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indeterminate moment problems
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Stieltjes-Wigert polynomials
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harmonic oscillator
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