V. A. Derkach

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Articles: 6

On a class of generalized Stieltjes continued fractions

Vladimir Derkach, Ivan Kovalyov

↓ Abstract   |   Article (.pdf)

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

Vladimir Derkach

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

Operator models associated with singular perturbations

Henk de Snoo, Vladimir Derkach, Seppo Hassi

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

Generalized resolvents of symmetric operators and admissibility

H. S. V. de Snoo, V. A. Derkach, S. Hassi, M. M. Malamud

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

Operator models associated with Kac subclasses of generalized Nevanlinna functions

Henk de Snoo, Vladimir Derkach, Seppo Hassi

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

On Krein space symmetric linear relations with gaps

Vladimir Derkach

Methods Funct. Anal. Topology 4 (1998), no. 2, 16-40


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