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The classical Krein-Naimark formula establishes a one-to-one correspondence between the generalized resolvents of a closed symmetric operator in a Hilbert space and the class of Nevanlinna familiesâ€¦ (More)

Let Ãƒ be a self-adjoint extension in KÌƒ of a fixed symmetric operator A in K âŠ† KÌƒ. An analytic characterization of the eigenvalues of Ãƒ is given in terms of the Q-function and the parameter functionâ€¦ (More)

- Jussi Behrndt
- 2006

We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally hasâ€¦ (More)

Trace formulae and singular values of resolvent power differences of self-adjoint elliptic operators

- Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik
- J. London Math. Society
- 2013

In this note self-adjoint realizations of second order elliptic differential expressions with non-local Robin boundary conditions on a domain Î© âŠ‚ Rn with smooth compact boundary are studied. Aâ€¦ (More)

We study a Sturm-Liouville expression with indefinite weight of the form sgn (âˆ’d2/dx2 +V ) on R and the non-real eigenvalues of an associated selfadjoint operator in a Krein space. For real-valuedâ€¦ (More)

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and âˆž areâ€¦ (More)

For closed linear operators or relations A and B acting between Hilbert spaces H and K the concepts of compact and finite rank perturbations are defined with the help of the orthogonal projections PAâ€¦ (More)

Spectral properties of singular Sturm-Liouville operators of the form A = sgn (Â·)(âˆ’ d 2 dx + V ) with the indefinite weight x 7â†’ sgn (x) on R are studied. For a class of potentials with lim|x|â†’âˆž Vâ€¦ (More)

The main objective of this paper is to give a rigorous treatment of Wignerâ€™s and Eisenbudâ€™s R-matrix method for scattering matrices of scattering systems consisting of two selfadjoint extensions ofâ€¦ (More)

- Jussi Behrndt, Till Micheler
- Journal of functional analysis
- 2014

This paper consists of two parts. In the first part, which is of more abstract nature, the notion of quasi-boundary triples and associated Weyl functions is developed further in such a way that itâ€¦ (More)