Extension of the Stieltjes moment sequence to the left and related problems of the spectral theory of inhomogeneous string
For a nonhomogeneous string with the known mass distribution (the full mass is assumed to be infinite), the known finite length, and the unknown spectral measure $d\sigma(t)$, we construct an analogous string with spectral measure $d\sigma(t)/t$. This allows to calculate the moments of all negativ...
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| Date: | 2007 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2007
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3347 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | For a nonhomogeneous string with the known mass distribution (the full mass is assumed to be infinite),
the known finite length, and the unknown spectral measure $d\sigma(t)$, we construct an analogous string with spectral measure $d\sigma(t)/t$.
This allows to calculate the moments of all negative orders of the measure $d\sigma(t)$.
The mechanical interpretation of the Stieltjes investigations on the moment problem proposed by M. G. Krein enables one to solve the following problem: for given
Stieltjes moment sequence with unique solution, calculate the moments of negative orders.
This problem is equivalent to the following one: establish the asymptotic behavior of the associate Stieltjes function near zero if its asymptotic behavior near infinity is given.
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