On The Basis Properties And Convergence Of Expansions In Terms Of Eigenfunctions For A Spectral Problem With A Spectral Parameter In The Boundary Condition

Abstract

In this paper, we consider the spectral problem − y 00 + q (x) y = λy, 0 < x < 1, y (0) = 0, y0 (0) − dλy (1) = 0, where λ is a spectral parameter, q (x) ∈ L1 (0, 1) is a complex-valued function and d is an arbitrary nonzero complex number. We study the spectral properties ( asymptotic formulae for eigenvalues and eigenfunctions, minimality and basicity of the system of eigenfunctions, the uniform convergence of expansions in terms of eigenfunctions ) of the considered boundary value problem.