# V. A. Derkach

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Articles: 6

### On a class of generalized Stieltjes continued fractions

Methods Funct. Anal. Topology 21 (2015), no. 4, 315-335

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 fraction that, in the case when ${\mathbf s}=\{s_j\}_{j=0}^\infty$ is a sequence of moments of a probability measure on $\mathbb R_+$, coincide with the $J-$fraction and the Stieltjes fraction, respectively. A subclass $\mathcal H^{reg}$ of regular sequences is specified for which explicit formulas connecting these two continued fractions are found. For ${\mathbf s}\in\mathcal H^{reg}$ the Darboux transformation of the corresponding generalized Jacobi matrix is calculated in terms of the generalized Stieltjes fraction.

### On indefinite abstract interpolation problem

Methods Funct. Anal. Topology 7 (2001), no. 4, 87-100

### Operator models associated with singular perturbations

Methods Funct. Anal. Topology 7 (2001), no. 3, 1-21

### Generalized resolvents of symmetric operators and admissibility

Methods Funct. Anal. Topology 6 (2000), no. 3, 24-55

Let A be a symmetric linear operator (or relation) with equal, possibly infinite, defect numbers. It is well know that one can associate with A a boundary value space and the Weyl function M(λ). The authors show that certain fractional-linear transforms of M(λ) are identified as Weyl functions of extensions of A, and vice versa. This connection is applied to various problems arising in the extension theory of symmetric operators. Some new criteria for a linear operator to be selfadjoint are established. When the defect numbers of A are finite the structure of all selfadjoint extensions with an exit space is completely characterized via a pair of boundary value spaces and their respective Weyl functions. New admissibility criteria are given which guarantee that a generalized resolvent of a nondensely defined symmetric operator corresponds to a selfadjoint operator extension.

### Operator models associated with Kac subclasses of generalized Nevanlinna functions

Methods Funct. Anal. Topology 5 (1999), no. 1, 65-87