ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 34, 46, 47 Malamud, Mark Michael, University of Donetsk, Ukraine Inverse spectral analysis for first order systems Different kinds of inverse spectral problems for first order systems

(1)  −iB ⊗ \frac{dy}{dx} + Q(x)y = λy, y = col(y_{1}, ..., y_{n})

on a finite segment and semiaxis are considered. Borg type problems as well as inverse problems with partial information on the potential matrix Q are investigated. A solution to the inverse spectral problem for systems (1) on the half line is also provided. Namely, necessary and sufficient conditions for a matrix measure to be a spectral function of a self-abjoint boundary value problem for a system (1) on L_{2}[0, ∞) will be presented. Part of these results is joint work with J. Brüning and M. Lesch.