Hill's equation systems and infinite determinants
R. Denk
Abstract. In this paper we develop a method to calculate the Floquet exponents of the matrix-valued version of Hill's equation using infinite determinants. It is shown that the Floquet exponents are precisely the zeros of an infinite determinant corresponding to the differential equation. The proof of this result uses the continuity and holomorphy of the infinite determinant.
Math. Nachr. 175 (1995), 47-60.
The paper is available here: pdf