The d-dimensional discrete Schrödinger operator whose potential is supported on the subspace Zd2 of Zd is considered: H = Ha+VM , where Ha = H0+Va, H0 is the d-dimensional discrete Laplacian, Va is a constant “surface” potential, Va(x) = aδ(x1), x = (x1, x2), x1 ∈ Zd1 , x2 ∈ Zd2 , d1 + d2 = d, and VM (x) = gδ(x1) tanπ(α · x2 + ω) with α ∈ Rd2 , ω ∈ [0, 1). It is proved that if the components of...

Let (X,%, ß) be a u-finite measure space and 3£ be a linear subspace of S?x{ft) with supp^ = X. The following inverse problem is treated: Which sets A £ 21 are "^-determined" within the class of all functions g e S? ...