On the nonself - adjoint ordinary differential operators with periodic boundary conditions
YazarVeliev, Oktay A.
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KünyeVELIEV, O. (2010). On the nonself - adjoint ordinary differential operators with periodic boundary conditions. Israel Journal of Mathematics, 176 (1), pp. 195-207. http://dx.doi.org/10.1007/s11856-010-0025-x.
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the nonself-adjoint ordinary differential operator with periodic and antiperiodic boundary conditions, when coefficients are arbitrary summable complex-valued functions. Then using these asymptotic formulas, we obtain necessary and sufficient conditions on the coefficient for which the root functions of these operators form a Riesz basis.