2017
Том 69
№ 9

All Issues

Extension of the Stieltjes moment sequence to the left and related problems of the spectral theory of inhomogeneous string

Nudel'man A. A.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 6, pp 894-906.

Citation Example: Nudel'man A. A. Extension of the Stieltjes moment sequence to the left and related problems of the spectral theory of inhomogeneous string // Ukr. Mat. Zh. - 2007. - 59, № 6. - pp. 815–825.

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