2017/03/01 by Belishev, M. I., Simonov, S. A.
#06B35 #34A55 #47-XX #47A46 #FOS: Mathematics #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1703.00176
The notion of the wave spectrum of a semi-bounded symmetric operator was introduced by one of the authors in 2013. The wave spectrum is a topological space determined by the operator in a canonical way. The definition uses a dynamical system associated with the operator: the wave spectrum is constructed from its reachable sets. In the paper we give a description of the wave spectrum of the operator L0=-(d2)/(dx2)+q which acts in the space L2(0,∞) and has defect indices (1,1). We construct a functional (wave) model of the operator L0^* in which the elements of the original L2(0,∞) are realized as functions on the wave spectrum. It turns out to be identical to the original L0^*. The latter is fundamental in solving inverse problems: the wave model is determined by their data, which allows for reconstruction of the original.