SINGULAR CONTINUOUS SPECTRUM OF HALF-LINE SCHRODINGER OPERATORS WITH POINT INTERACTIONS ON A SPARSE SET

We say that a discrete set X = {x(n)}(n is an element of N0) on the half-line 0 = x(0) < x(1) < x(2) < x(3) < ....< x(n) <...< +infinity is sparse if the distances Delta x(n) = x(n+)1-x(n) between neighbouring points satisfy the condition Delta x(n) /x(n-1)->+infinity. In this paper half-line Schrdinger operators with point delta-and delta'-interactions on a sparse set are considered. Assuming that strengths of point interactions tend to 1 we give simple sufficient conditions for such Schrdinger operators to have non-empty singular continuous spectrum and to have purely singular continuous spectrum, which coincides with R+.