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- W2963561522 abstract "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 $L_0=-frac{d^2}{dx^2}+q$ which acts in the space $L_2(0,infty)$ and has defect indices $(1,1)$. We construct a functional (wave) model of the operator $L_0^*$ in which the elements of the original $L_2(0,infty)$ are realized as functions on the wave spectrum. It turns out to be identical to the original $L_0^*$. The latter is fundamental in solving inverse problems: the wave model is determined by their data, which allows for reconstruction of the original." @default.
- W2963561522 created "2019-07-30" @default.
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- W2963561522 date "2018-03-12" @default.
- W2963561522 modified "2023-09-26" @default.
- W2963561522 title "Wave model of the Sturm–Liouville operator on the half-line" @default.
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- W2963561522 doi "https://doi.org/10.1090/spmj/1491" @default.
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