Tbilisi Mathematical Journal

Spectral analysis of non-selfadjoint matrix Schrödinger equation on the half-line with general boundary condition at the origin

G. Mutlu

We examine the spectral properties of the non-selfadjoint matrix Schrödinger equation on the half-line
-y^" + Q(x)y=k²y, x ∈ R₊,
where n x n matrix potential is symmetric but not Hermitian for each x ∈ R₊, each entry of the matrix Q is a complex-valued, Lebesgue measurable function on x ∈ R₊ with a finite first moment. We impose the most general boundary condition at the origin
Ay(0) + By^'(0) = 0,
such that the constant n x n matrices A and B satisfy
AB^T - BA^T = 0, Rank [A|B]=n.
We obtain the resolvent operator, the point spectrum, continuous spectrum and the set of spectral singularities of the resulting non-selfadjoint matrix Schrödinger operator.


Tbilisi Mathematical Journal, Special Issue (8 - 2021), pp. 227-236