39 citations · 169 across the 20 of their papers we have counts for
22 papers
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…
Spectral analysis and domain truncation methods for Maxwell's equations
Sabine Boegli, Francesco Ferraresso, Marco Marletta +1
We analyse how the spectrum of the anisotropic Maxwell system with bounded conductivity on a Lipschitz domain is approximated by domain truncation. First we prove a new non-convex…
Pseudo Numerical Ranges and Spectral Enclosures
Borbala Gerhat, Christiane Tretter
We introduce the new concepts of pseu\-do numerical range for operator functions and families of sesquilinear forms as well as the pseu\-do block numerical range for o…
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…
On a spectral problem in magnetohydrodynamics and its relevance for the geodynamo
Frank Stefani, Christiane Tretter
One of the most remarkable features of the geodynamo is the irregular occurrence of magnetic field reversals. Starting with the operator theoretical treatment of a non-selfadjoint…
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…
Essential spectrum of elliptic systems of pseudo-differential operators on
Orif O. Ibrogimov, Christiane Tretter
Inspired by a result of Wong (Commun. Partial Differ. Equ. 13(10):1209-1221, 1988), we establish an analytic description of the essential spectrum of non-self-adjoint mixed-order s…
On the spectrum of an operator in truncated Fock space
Orif O. Ibrogimov, Christiane Tretter
We study the spectrum of an operator matrix arising in the spectral analysis of the energy operator of the spin-boson model of radioactive decay with two bosons on the torus. An an…
Dirac-Krein systems on star graphs
Vadym Adamyan, Heinz Langer, Christiane Tretter +1
We study the spectrum of a self-adjoint Dirac-Krein operator with potential on a compact star graph with a finite number of edges. This operator is defined by a Di…
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…
Approximations of spectra of Schrödinger operators with complex potentials on
Sabine Bögli, Petr Siegl, Christiane Tretter
We study spectral approximations of Schrödinger operators with complex potentials on , or exterior domains , by domain truncation. O…
Analysis of the essential spectrum of singular matrix differential operators
Orif O. Ibrogimov, Petr Siegl, Christiane Tretter
A complete analysis of the essential spectrum of matrix-differential operators of the form \begin{align} \begin{pmatrix} -\displaystyle{\frac{\rm d}{\rm d t}} p \displ…
Non-linear eigenvalue problems and applications to photonic crystals
Christian Engström, Heinz Langer, Christiane Tretter
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these…
Essential spectrum of systems of singular differential equations
Orif O. Ibrogimov, Heinz Langer, Matthias Langer +1
In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics…
Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati Equations
Christiane Tretter, Christian Wyss
An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the H…
Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings
Vyacheslav Pivovarchik, Natalia Rozhenko, Christiane Tretter
We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root…
Eigenvalue estimates for non-selfadjoint Dirac operators on the real line
Jean-Claude Cuenin, Ari Laptev, Christiane Tretter
We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential lie in the disjoint union of two disks in the right and left half…
Simplicity of extremal eigenvalues of the Klein-Gordon equation
Mario Koppen, Christiane Tretter, Monika Winklmeier
We consider the spectral problem associated with the Klein-Gordon equation for unbounded electric potentials. If the spectrum of this problem is contained in two disjoint real inte…
On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator
Uwe Guenther, Heinz Langer, Christiane Tretter
The existence of magnetohydrodynamic mean-field alpha^2-dynamos with spherically symmetric, isotropic helical turbulence function alpha is related to a non-self-adjoint spectral pr…
Bounds on the spectrum and reducing subspaces of a J-self-adjoint operator
Sergio Albeverio, Alexander K. Motovilov, Christiane Tretter
Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint operator commuting with J and…