Absence of singular continuous spectrum of selfadjoint operators (2012)
Spectral analysis is a powerful tool for study of properties of differential operators in mathematical physics, in particular in quantum mechanics. The aim of this paper is to give an introduction to the theory of linear operators on Banach and Hilbert spaces, to study the spectral properties of selfadjoint operators on a Hilbert space and to apply some classic results that provide conditions for the absence of singular continuous spectrum of certain selfadjoint operator. Finally, these results are applied to the Schrödinger operators with potential in L2(Rm)