Vladimir Ryzhov
Symmetric Functional Model for Extensions of Hermitian
Operators
(519K, PDF)
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.