We consider the periodic weighted operator T y = ? ?2 (2 y 0) 0 in L 2 (R; (x) 2 dx), where is a 1-periodic real positive function with (0) = 1. We assume q = 0 == 2 L 2 (0; 1). The spectrum of T consists of intervals n = + n?1 ; ? n ] separated by gaps (? n ; + n); n > 1. Using essentially the square of the gap lengths, the centre of the gap and the Dirichlet eigenvalues on the unit interval w...
