Abstract
Nonlocal spectral problem for a second-order differential equation with an involutionFor the spectral problem -u (x) + αu (-x) = λu(x), -1 < x < 1, with nonlocal boundary conditions u(-1) = βu(1), u (-1) = u (1), where α ∈ (-1, 1), β 2 = 1, we study the spectral properties.We show that if r = (1 -α)/(1 + α) is irrational, then the system of eigenfunctions is complete and minimal in L2(-1, 1) but is not a basis.In the case of a rational number r, the root subspace of the problem consists of eigenvectors and an infinite number of associated vectors.In this case, we indicated a method for choosing associated functions that provides the system of root functions of the problem is an unconditional basis in L2(-1, 1).