n y ∈ H2(R \ Γ) ¯̄ ̄

In this talk we study the spectral gaps of the one-dimensional Schrödinger operators with particular periodic point interactions. We fix κ ∈ (0, π) ∪ (π, 2π). Let Γ1 = 2πZ, Γ2 = {κ}+ 2πZ, Γ = Γ1 ∪ Γ2. For θ1, θ2 ∈ [−π/2, π/2) andA1, A2 ∈ SO(2)\{±I}, we define the operatorH = H(θ1, θ2, A1, A2) in L2(R) as follows