Abstract
The inverse problem for canonical differential equations is investigated for Hamiltonians with singularities. The usual notion of a spectral function is not adequate in this generality, and it is replaced by a more general notion of spectral data. The method of operator identities is used to describe a solution of the inverse problem in this setting. The solution is explicitly computable in many cases, and a number of examples are constructed.
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Rovnyak, J., Sakhnovich, L.A. (2007). Inverse Problems for Canonical Differential Equations with Singularities. In: Ball, J.A., Eidelman, Y., Helton, J.W., Olshevsky, V., Rovnyak, J. (eds) Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, vol 179. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8539-2_16
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