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where λ is a real parameter. This equation has two solutions y1(x, λ) and y2(x, λ) which are uniquely determined by the initial conditions y1(+0, λ) = 1, y′ 1(+0, λ) = 0, and y2(+0, λ) = 0, y′ 2(+0, λ) = 1, respectively. We introduce the discriminant D(λ) of the equation (1): D(λ) = y1(2π + 0, λ) + y′ 2(2π + 0, λ). (2) Let λj be the (j + 1)st zero of D(·)2 − 4. Then we have λ0 < λ1 ≤ λ2 < λ3 ≤ λ4 < · · · < λ2k−1 ≤ λ2k < · · · → ∞. We define Bj = [λ2j−2, λ2j−1], Gj = (λ2j−1, λ2j). Then we derive

Identification of the absent spectral gaps in a class of generalized Kronig-Penney Hamiltonians