06-143 Vladimir Ryzhov

Symmetric Functional Model for Extensions of Hermitian Operators (519K, PDF) May 1, 06

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Abstract. This paper offers the functional model of a class of non-selfadjoint extensions of a Hermitian operator with equal deficiency indices. The explicit form of dilation of a dissipative extension is offered and the symmetric form of Sz.Nagy-Foia\c{s} model as developed by B.~Pavlov is constructed. A variant of functional model for a general non-selfadjoint non-dissipative extension is formulated. We illustrate the theory by two examples: singular perturbations of the Laplace operator in~$L_2(\Real^3)$ by a finite number of point interactions, and the Schr\"odinger operator on the half axis~$(0, \infty)$ in the Weyl limit circle case at infinity.

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