This article is cited in 10 papers

Solution of the Inverse Quasiperiodic Problem for the Dirac System

I. M. Nabiev<sup>ab

a</sup> Baku State University
^b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: We present a complete solution of the inverse problem of spectral analysis for the Dirac operator with quasiperiodic boundary conditions. We prove a uniqueness theorem for the solution of the inverse problem and obtain necessary and sufficient conditions for a sequence of real numbers to be the spectrum of a quasiperiodic Dirac problem.

Keywords: inverse spectral problem, Dirac operator, quasiperiodic Dirac problem, Lyapunov function, boundary-value problem, spectral data, Bernstein's inequality.

UDC: 517.984

Received: 02.12.2009
Revised: 13.05.2010

DOI: 10.4213/mzm8657

 English version: Mathematical Notes, 2011, 89:6, 845–852

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