Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Roitberg, I."'
Autor:
Roitberg, I., Sakhnovich, A. L.
Publikováno v:
Integral Equations Operator Theory 91:6 (2019), Art. 50
We generalize the notion of the Arov-Krein entropy functional for the case of generalized Nevanlinna functions and obtain a representation of these functionals on solutions of indefinite interpolation problems. The case of indefinite Caratheodory pro
Externí odkaz:
http://arxiv.org/abs/1904.04277
Publikováno v:
J. Difference Equ. Appl. 25 (2019), pp. 294--304
We consider the cases of the self-adjoint and skew-self-adjoint discrete Dirac systems, obtain explicit expressions for reflection coefficients and show that rational reflection coefficients and Weyl functions coincide.
Comment: In this paper, w
Comment: In this paper, w
Externí odkaz:
http://arxiv.org/abs/1806.03632
Autor:
Roitberg, I. Ya., Sakhnovich, A. L.
Publikováno v:
Zh. Mat. Fiz. Anal. Geom. 14 (2018), issue 4 dedicated to V.A. Marchenko, pp. 532--548
We consider discrete self-adjoint Dirac systems determined by the potentials (sequences) $\{C_k\}$ such that the matrices $C_k$ are positive definite and $j$-unitary, where $j$ is a diagonal $m\times m$ matrix and has $m_1$ entries $1$ and $m_2$ entr
Externí odkaz:
http://arxiv.org/abs/1802.10557
Publikováno v:
J. Phys. A: Math. Theor. 51 (2018) 015202
We consider continuous and discrete Schr\"odinger systems with self-adjoint matrix potentials and with additional dependence on time (i.e., dynamical Schr\"odinger systems). Transformed and explicit solutions are constructed using our generalized (GB
Externí odkaz:
http://arxiv.org/abs/1701.08011
Publikováno v:
Linear Algebra and its Applications, 533 (2017) 428-450
Procedures to recover explicitly discrete and continuous skew-selfadjoint Dirac systems on semi-axis from rational Weyl matrix functions are considered. Their stability is shown. Some new facts on asymptotics of pseudo-exponential potentials (i.e., o
Externí odkaz:
http://arxiv.org/abs/1510.00793
Publikováno v:
Oper. Matrices 8 (2014), 799-819
A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur coefficients
Externí odkaz:
http://arxiv.org/abs/1206.2915
Publikováno v:
Integral Equations and Operator Theory, 74:2 (2012), 163--187
A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg-Marchenko type uniqueness result and the
Externí odkaz:
http://arxiv.org/abs/1112.1325
Publikováno v:
Inverse Problems 28 (2012), 015010, 18pp
Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are treated for such W
Externí odkaz:
http://arxiv.org/abs/1106.1263
Publikováno v:
Indagationes Mathematicae 23 (2012), 690-700
The structured operators and corresponding operator identities, which appear in inverse problems for the self-adjoint and skew-self-adjoint Dirac systems with rectangular potentials, are studied in detail. In particular, it is shown that operators wi
Externí odkaz:
http://arxiv.org/abs/1106.0812
Publikováno v:
Oper. Matrices 7:1 (2013), 183-196
A non-classical Weyl theory is developed for Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and the corresponding direct problem is treated. Furthermore, explicit solutions of the direct and inverse pr
Externí odkaz:
http://arxiv.org/abs/1105.2013