arXiv Analytics

Sign in

arXiv:0912.4340 [math.SP]AbstractReferencesReviewsResources

On the Basis Property of the Root Functions of Differential Operators with Matrix Coefficients

O. A. Veliev

Published 2009-12-22Version 1

We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas, we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions of the operator under consideration forms a Riesz basis.

Related articles: Most relevant | Search more
arXiv:math/0403226 [math.SP] (Published 2004-03-14)
On the discrete spectrum of a family of differential operators
arXiv:1309.1751 [math.SP] (Published 2013-09-06)
Asymptotic formulas for spectral gaps and deviations of Hill and 1D Dirac operators
arXiv:1106.5774 [math.SP] (Published 2011-06-28)
Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators