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Published in:
2007 | OriginalPaper | Chapter
Functional Model of a Class of Non-selfadjoint Extensions of Symmetric Operators
Author : Vladimir Ryzhov
Published in: Operator Theory, Analysis and Mathematical Physics
Publisher: Birkhäuser Basel
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This paper offers the functional model of a class of non-selfadjoint extensions of a symmetric operator with equal deficiency indices. The explicit form of dilation of a dissipative extension is offered and the Sz.-Nagy-Foiaş model as developed by B. Pavlov is constructed. A variant of functional model for a non-selfadjoint non-dissipative extension is formulated. We illustrate the theory by two examples: singular perturbations of the Laplace operator in
L
2
(ℝ
3
) by a finite number of point interactions, and the Schrödinger operator on the half-axis (0, ∞) in the Weyl limit circle case at infinity.