HARRY HOCHSTADT The purpose of this note is to state and prove the following theorem. Theorem. Consider the Hill's equation (1) y" +[a + q(t)]y = 0, where q(t+ir) =q(t), and q(t) is bounded. Let X, denote the ith eigenvalue corresponding to which a solution of (1) has period t, and X' those corresponding to which (1) has a solution of period 2ir. It is well known [l] that for these eigenvalues Xo < Ai" Ú \l < Xi ^ X2 < X8' Û \í < X3 á X4 < • • • and for all X in the intervals (2) (Xo, X/), (Xa… CONTINUE READING