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arXiv · 1703.06220

Functional model for extensions of symmetric operators and applications to scattering theory

Kirill D. Cherednichenko·Alexander V. Kiselev·Luis O. Silva
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Abstract

On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the scattering matrix for pairs of such extensions. We use this representation to explicitly recover the coupling constants in the inverse scattering problem for a finite non-compact quantum graph with $\delta$-type vertex conditions.

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Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva. 2017-03-18. Functional model for extensions of symmetric operators and applications to scattering theory. https://doi.org/10.3934/nhm.2018009

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