Equality of multiplicities of a Sturm–Liouville eigenvalue

We give a new and unified proof of the fact that for any eigenvalue of a self-adjoint Sturm– Liouville problem with limit-circle end points, its analytic and geometric multiplicities are equal. This proof is geometric in nature and can be generalized to the case of high-order differential equations.  2004 Elsevier Inc. All rights reserved.