Singular continuous spectrum of half-line Schrodinger operators with point interactions on a sparse set

Abstract

Tyt. z nagłówka.Bibliogr. s. 627-628.Dostępny również w formie drukowanej.ABSTRACT: We say that a discrete set X = {xn}n Є N0 on the half-line 0 = x0 < x1< x2< x3 < ...< xn <...< +∞ is sparse if the distances Δxn = xn+1-xn between neighbouring points satisfy the condition [formula]. In this paper half-line Schrödinger operators with point δ- and δ'- interactions on a sparse set are considered. Assuming that strengths of point interactions tend to ∞ we give simple sufficient conditions for such Schrödinger operators to have non-empty singular continuous spectrum and to have purely singular continuous spectrum, which coincides with R+. KEYWORDS: half-line schrodinger operators, delta-interactions, delta'-interactions, singular continuous spectrum