Spectral Asymtotic Behavior for a Class of Schrodinger Operators on 1-dimensional Fractal Domains

Abstract

In this paper, we study the spectral asymptotic behavior for a class of Schrödinger operators on 1-dimensional fractal domains. We have obtained, if the potential function is locally constant, the exact second term of the spectral asymptotics. In general, we give a sharp estimate for the second term of the spectral asymptotics.