6 papers · 1 filter
Computing Klein-Gordon Spectra
Frank Rösler, Christiane Tretter
We study the computational complexity of the eigenvalue problem for the Klein-Gordon equation in the framework of the Solvability Complexity Index Hierarchy. We prove that the eige…
Everything is possible for the domain intersection dom T \cap dom T*
Yury Arlinskii, Christiane Tretter
This paper shows that for the domain intersection $\dom T\cap\dom T^*$ of a closed linear operator and its Hilbert space adjoint everything is possible for very common classes of o…
The essential numerical range for unbounded linear operators
Sabine Bögli, Marco Marletta, Christiane Tretter
We introduce the concept of essential numerical range for unbounded Hilbert space operators and study its fundamental properties including possible equivalent char…
The damped wave equation with unbounded damping
Pedro Freitas, Petr Siegl, Christiane Tretter
We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a cont…
Numerical Range and Quadratic Numerical Range for Damped Systems
Birgit Jacob, Christiane Tretter, Carsten Trunk +1
We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations $\ddot{z}(t) + D \dot{z} (t) + A_0 z(t) = 0…
Non-symmetric perturbations of self-adjoint operators
Jean-Claude Cuenin, Christiane Tretter
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or inf…