Abstract
Supersingular H-n rank one perturbations of an arbitrary positive self-adjoint operator A acting in the Hilbert space H are investigated. The operator corresponding to the formal expression A(alpha) = A + alpha(phi,.)phi, alpha is an element of R, phi is an element of H-n (A), is determined as a regular operator with pure real spectrum acting in a certain extended Hilbert space H superset of X The resolvent of the operator so defined is given by a certain generalization of Krein's resolvent formula. It is proven that the spectral properties of the operator are described by generalized Nevanlinna functions. The results of [24] are extended to the case of arbitrary integer n greater than or equal to 4.
Original language | English |
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Pages (from-to) | 437-460 |
Journal | Integral Equations and Operator Theory |
Volume | 45 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2003 |
Subject classification (UKÄ)
- Mathematics
Free keywords
- singular perturbations
- Krein's formula
- Nevanlinna functions