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

  • * Corresponding author: Kirill D. Cherednichenko

    * Corresponding author: Kirill D. Cherednichenko 

To the memory of Professor Boris Pavlov

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  • 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 $δ$-type vertex conditions.

    Mathematics Subject Classification: 47A45, 34L25, 81Q35.


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