2019
Том 71
№ 7

All Issues

Nudel'man A. A.

Articles: 3
Article (Russian)

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

Nudel'man A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 6. - pp. 815–825

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.

Article (Russian)

Criterion of unitary similarity of minimal passive scattering systems with a given transfer function

Arov D. Z., Nudel'man A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 2. - pp. 147-156

We establish necessary and sufficient conditions under which all minimal passive scattering systems that have a given transfer operator function are unitarily equivalent. These conditions can be significantly simplified in special cases important for applications, in particular, in the case where a transfer function is rational and in a more general case where this function is pseudoextendable.

Article (Ukrainian)

On M. G. Krein's contribution to the moment problem

Nudel'man A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 1-2. - pp. 63–75