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Publications at the institute since 1990

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Philipp, Friedrich; Szafraniec, Franciszek Hugon; Trunk, Carsten
Selfadjoint operators in S-spaces. - In: Journal of functional analysis - Amsterdam [u.a.] : Elsevier, ISSN 1096-0783, Bd. 260 (2011), 4, S. 1045-1059

We study S-spaces and operators therein. An S-space is a Hilbert space with an additional inner product given by $\Skindef := (U\,\cdot\,,-)$, where $U$ is a unitary operator. We investigate spectral properties of selfadjoint operators in S-spaces. We show that their spectrum is symmetric with respect to the real axis. As a main result we prove that for each selfadjoint operator $A$ in an S-space we find an inner product which turns $\bez$ into a Krein space and $A$ into a selfadjoint operator therein. As a consequence we get a new simple condition for the existence of invariant subspaces of selfadjoint operators in Krein spaces, which provides a different insight into this well know and in general unsolved problem.



http://dx.doi.org/10.1016/j.jfa.2010.10.023
Azizov, Tomas Ya.; Behrndt, Jussi; Jonas, Peter; Trunk, Carsten
Spectral points of definite type and type π for linear operators and relations in Krein spaces. - In: Journal of the London Mathematical Society - Oxford : Wiley, ISSN 1469-7750, Bd. 83 (2011), 3, S. 768-788

Spectral points of positive and negative type, and type $\pi_{+}$ and type $\pi_{-}$ for closed linear operators and relations in Krein spaces are introduced with the help of approximative eigensequences. The main objective of the paper is to study these sign type properties in the non-selfadjoint case under various kinds of perturbations, e.g. compact perturbations and perturbations small in the gap metric. Many of the obtained perturbation results are also new for the special case of bounded and unbounded selfadjoint operators in Krein spaces.



http://dx.doi.org/10.1112/jlms/jdq098
Behrndt, Jussi; Hassi, Seppo; Snoo, Henk; Wietsma, Rudi; Winkler, Henrik
Linear fractional transformations of Stieltjes functions. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 11 (2011), 1, S. 887-888

http://dx.doi.org/10.1002/pamm.201110430
Babovsky, Hans;
Numerical simulation of the Boltzmann equation: deterministic vs. Monte Carlo schemes. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 11 (2011), 1, S. 759-760

http://dx.doi.org/10.1002/pamm.201110369
Hennig, Eckhard; Krauße, Dominik; Schäfer, Eric; Sommer, Ralf; Trunk, Carsten; Winkler, Henrik
Frequency compensation for a class of DAE's arising in electrical circuits. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 11 (2011), 1, S. 837-838

Structured perturbations of regular pencils of the form $sE-A$, $E,A\in\dR^{n\times n}, ˜s\in\dC,$ are considered which model the addition of a capacitance $c$ in an electrical circuit in order to improve the frequency response.



http://dx.doi.org/10.1002/pamm.201110407
Wozniak, Sander; Gerlach, Tobias; Schäfer, Günter
Optimization-based secure multi-hop localization in wireless ad hoc networks. - In: 17th GI/ITG Conference on Communication in Distributed Systems (KiVS 2011) : March 8 - 11, 2011, Kiel, Germany. - Wadern : Schloss Dagstuhl - Leibniz-Zentrum für Informatik, ISBN 978-3-939897-27-9, (2011), S. 182-187

http://dx.doi.org/10.4230/OASIcs.KiVS.2011.182
Winkler, Henrik; Behrndt, Jussi; Hassi, Seppo; Snoo, Henk; Wietsma, Rudi
Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator - Ilmenau : Techn. Univ., Inst. für Mathematik, 2011 - Online-Ressource (PDF-Datei: 26 S., 436,5 KB). . - (Preprint. - M11,18)
http://www.db-thueringen.de/servlets/DocumentServlet?id=19505
Winkler, Henrik; Woracek, Harald
Reparametrizations of non trace-normed Hamiltonians - Ilmenau : Techn. Univ., Inst. für Mathematik, 2011 - Online-Ressource (PDF-Datei: 23 S., 344,7 KB). . - (Preprint. - M11,17)

We consider a Hamiltonian system of the form y0(x) = JH(x)y(x), with a locally integrable and nonnegative 2_2-matrix valued Hamiltonian H(x). In the literature dealing with the operator theory of such equations, it is often required in addition that the Hamiltonian H is trace{normed, i.e. satis_es trH(x) _ 1. However, in many examples this property does not hold. The general idea is that one can reduce to the trace{normed case by applying a suitable change of scale (reparametrization). In this paper we justify this idea and work out the notion of reparametrization in detail.



http://www.db-thueringen.de/servlets/DocumentServlet?id=19504
Knobloch, Jürgen; Rieß, Thorsten; Vielitz, Martin
Nonreversible homoclinic snaking. - In: Dynamical systems : an international journal. - London : Taylor & Francis, ISSN 1468-9375, Bd. 26 (2011), 3, S. 335-365

http://dx.doi.org/10.1080/14689367.2011.592488
Hildenbrandt, Regina;
A k-server problem with parallel requests and unit distances - Ilmenau : Techn. Univ., Inst. für Mathematik, 2011 - Online-Ressource (PDF-Datei: 11 S., 207,5 KB). . - (Preprint. - M11,16)

In the paper a k-server problem with parallel requests where several servers can also be located on one point is considered. We show that a HARMONIC_p k-server algorithm is competitive against an adaptive online adversary in case of unit distances.



http://www.db-thueringen.de/servlets/DocumentServlet?id=19013