Semiclassical asymptotics of the vector Sturm-Liouville problem (Q871767)

The paper deals with the matrix Sturm-Liouville problem on the whole line with a potential which is a smooth, self-adjoint matrix function, and with a small parameter at the derivatives. The goal is to study the asymptotics of eigenvalues and eigenfunctions in the case when the symbol of the problem has eigenvalues of variable multiplicity. The main result is that in the nonresonant case, the Born-Sommerfeld-Maslov quantization conditions provide the asymptotics of eigenvalues with quadratic precision, as in the case in which there is no modification of multiplicity. In the case of nontrivial multiplicity, the asymptotic behavior of the eigenfunctions is different.