We study a stepwise algorithm for solving the indefinite truncated moment problem and
obtain the factorization of the matrix describing the solution of this problem into elementary …

We develop direct and inverse spectral analysis for finite and semi-infinite non-self-adjoint
Jacobi matrices with a rank-one imaginary part. It is shown that given a set of n not …

Let J be a monic Jacobi matrix associated with the Cauchy transform F of a probability
measure. We construct a pair of the lower and upper triangular block matrices L and U such …

With each sequence of real numbers ${\mathbf s}=\{s_j\} _ {j= 0}^\infty $ two kinds of
continued fractions are associated,-the so-called $ P-$ fraction and a generalized Stieltjes …

The nondegenerate truncated indefinite Stieltjes moment problem in the class of
generalized Stieltjes functions is considered. To describe the set of solutions of this problem …

A bounded operator T in a separable Hilbert space ℌ is called quasi-selfadjoint if ker
(TT*)≠{0} and ℜ-quasi-selfadjoint if ℜ⊇ ran (TT*), where ℜ is a subspace of ℌ. An ℜ-quasi …

Let $\mathfrak {J} $ be a monic generalized Jacobi matrix, ie a three-diagonal block matrix of
special form, introduced by M.~ Derevyagin and V.~ Derkach in 2004. We find conditions for …

In this paper we prove Szegő's Theorem for the case when a finite number of Verblunsky
coefficients lie outside the closed unit disk. Although a form of this result was already proved …

The paper deals with two types of inverse spectral problems for the class of generalized
Jacobi matrices introduced in [9]. Following the scheme proposed in [5], we deduce analogs …

Let dμ be a probability measure on [0,+∞) such that its moments are finite. Then the Cauchy–
Stieltjes transform S of dμ is a Stieltjes function, which admits an expansion into a Stieltjes …