Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Marko Lindner
TU Chemnitz, TU Freiberg
Spectra and Finite Sections of Random Jacobi Operators
For a random singly- or bi-infinite Jacobi matrix A, we give upper and lower bounds on the spectrum and
present a version of the finite section method for the approximate solution of equations Ax = b that is
stable as soon as A is invertible.
Friedrich Philipp
Technische Universität Berlin
Bounds on the non-real spectrum of indefinite Sturm-Liouville operators
We consider indefinite Sturm-Liouville operators A of the form
(A f )(x) = sgn(x) � − f ′′ (x) + q(x) f (x) �
x ∈ R, f ∈ H 2 (R)
with an essentially bounded and real-valued potential q ∈ L ∞ (R). It is well-known that the non-real spectrum
of the operator A is bounded, consists of normal eigenvalues and can only accumulate to the compact
interval [m+,m−] (which might be the empty set if m+ > m−), where
m+ = liminf
x→∞ q(x) and m− = −liminf
x→−∞ q(x).
So far, the non-real spectrum of A could not be localized in quantitative terms. We tackle this problem by
proving an abstract result concerning bounded perturbations of non-negative operators in Krein spaces
and find explicit bounds on the non-real spectrum of the operator A. It should be mentioned that the
perturbation result is applicable to a large class of ordinary and partial differential operators with indefinite
weights. This is a joint work with J. Behrndt (TU Graz) and C. Trunk (TU Ilmenau).
Rainer Picard
Technische Universität Dresden
A Class of Time-Shift Invariant Evolutionary Equations with an Application to Acoustic Waves
with Impedance Type Boundary Conditions.
A well-posedness result for a time-shift invariant class of evolutionary operator equations is considered
and exemplified by an application to an impedance type initial boundary value problem for the system
of linear acoustics. The acoustic initial boundary value problem allows for dynamics (including memory
effects) in the domain as well as on the domain boundary. The application presented here is an improvement
on a previously presented model class.
188