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Non-Self-Adjoint Sturm–Liouville Operators with Matrix Potentials

O. A. Veliev

Dogus University

Abstract: We obtain asymptotic formulas for non-self-adjoint operators generated by the Sturm–Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which the system of root vectors of the operator under consideration forms a Riesz basis.

Keywords: Sturm–Liouville operator, non-self-adjoint operator, quasiperiodic boundary condition, Riesz basis, root function, Jordan chain, Bessel operator.

UDC: 517.953

Received: 05.08.2005

DOI: 10.4213/mzm3704

 English version: Mathematical Notes, 2007, 81:4, 440–448

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