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 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.