P29177

Weyl theory: procedures, stability, control and applications

Published works

A.L. Sakhnovich, Dynamical canonical systems and their explicit solutions,
Discrete and Continuous Dynamical Systems A 37:3 (2017) 551--561.

A.L. Sakhnovich, Dynamics of electrons and explicit solutions of Dirac-Weyl    systems, J. Phys. A: Math. Theor. 50 (2017), Paper 115201

A.L. Sakhnovich, Hamiltonian Systems and Sturm-Liouville Equations: Darboux Transformation and Applications,  Integral Equations Operator Theory 88 (2017) 535–557


B. Fritzsche, B. Kirstein, I.Ya. Roitberg, and  A.L.Sakhnovich,
Stability of the procedure of explicit recovery of skew-selfadjoint Dirac systems from rational Weyl matrix functions, Linear Algebra Appl.   533 (2017), 428–450;

A.L. Sakhnovich, On accelerants and their analogs, and on the characterization
of the rectangular Weyl functions for Dirac systems with locally square-integrable potentials on a semi-axis, pp. 393--406, In: Operator Theory Adv. Appl. (volume 263 dedicated to Heinz Langer), Birkhauser, Cham, 2018.

B. Fritzsche, B. Kirstein, I.Ya. Roitberg and A.L. Sakhnovich, Continuous and discrete dynamical Schroedinger systems: explicit solutions, J. Phys. A 51 (2018), Paper 015202,

A.L. Sakhnovich, Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions. J. Differential Equations 265 (2018), no. 10, 4820–4834

I. Roitberg and A.L. Sakhnovich, The discrete self-adjoint Dirac systems of general type: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and the stability of solving of the inverse problem. Zh. Mat. Fiz. Anal. Geom. 14 (2018), no. 4, 532–548.

A.L. Sakhnovich, GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems. Operator theory, analysis and the state space approach, 389–398, Oper. Theory Adv. Appl., 271, Birkhäuser/Springer, Cham, 2018.

A.L. Sakhnovich, New “Verblunsky-type” coefficients of block Toeplitz and Hankel matrices and of corresponding Dirac and canonical systems. J. Approx. Theory 237 (2019), 186–209.

J. Michor and A.L.Sakhnovich, GBDT and algebro-geometric approaches to explicit solutions and wave functions for nonlocal NLS. J. Phys. A 52 (2019), 025201, 24 pp.

B. Fritzsche, B.Kirstein, I.Ya. Roitberg and A.L. Sakhnovich,Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions. J. Difference Equ. Appl. 25 (2019), no. 2, 294–304.

A.L. Sakhnovich, On the structure of the inverse to Toeplitz-block Toeplitz matrices and of the corresponding polynomial reflection coefficients, Trans. Amer. Math. Soc., 372 (2019), no. 8, 5547–5570.

F. Gesztesy and A.L. Sakhnovich, The inverse approach to Dirac-type systems based on the A-function concept. J. Funct. Anal. 279 (2020), no. 6, 108609.

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