Publikationen Prof. Trunk

Publikationen der Mitarbeiter

Publikationen am Fachgebiet

Results: 170
Created on: Thu, 28 Mar 2024 23:09:10 +0100 in 0.0742 sec


Gernandt, Hannes; Trunk, Carsten
Eigenvalue placement for regular matrix pencils with rank one perturbations. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (15 Seiten). - (Preprint ; M16,01)

A regular matrix pencil sE-A and its rank one perturbations are considered. We determine the sets in \C\cup\{\infty\} which are the eigenvalues of the perturbed pencil. We show that the largest Jordan chains at each eigenvalue of sE-A may disappear and the sum of the length of all destroyed Jordan chains is the number of eigenvalues (counted with multiplicities) which can be placed arbitrarily in \C\cup\{\infty\}. We prove sharp upper and lower bounds of the change of the algebraic and geometric multiplicity of an eigenvalue under rank one perturbations. Finally we apply our results to a pole placement problem for a single-input differential algebraic equation with feedback.



http://www.db-thueringen.de/servlets/DocumentServlet?id=27311
Berger, Thomas; Trunk, Carsten; Winkler, Henrik
Linear relations and the Kronecker canonical form. - In: Linear algebra and its applications, ISSN 0024-3795, Bd. 488 (2016), S. 13-44

http://dx.doi.org/10.1016/j.laa.2015.09.033
Philipp, Friedrich; Trunk, Carsten
Spectral points of type π+ and type π- of closed operators in indefinite inner product spaces. - In: Operators and matrices, Bd. 9 (2015), 3, S. 481-506
Im Titel ist "+" und "-" tiefgestellt

http://dx.doi.org/10.7153/oam-09-30
Trunk, Carsten;
Locally definitizable operators: the local structure of the spectrum. - In: Operator theory, (2015), S. 241-259

Berger, Thomas; Trunk, Carsten; Trunk, Carsten *1968-*; Winkler, Henrik;
Linear relations and the Kronecker canonical form. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2015. - Online-Ressource (PDF-Datei: 27 S., 402 KB). - (Preprint ; M15,05)

We show that the Kronecker canonical form (which is a canonical decomposition for pairs of matrices) is the representation of a linear relation in a finite dimensional space. This provides a new geometric view upon the Kronecker canonical form. Each of the four entries of the Kronecker canonical form has a natural meaning for the linear relation which it represents. These four entries represent the Jordan chains at finite eigenvalues, the Jordan chains at infinity, the so-called singular chains and the multi-shift part. Or, to state it more concise: For linear relations the Kronecker canonical form is the analogue of the Jordan canonical form for matrices.



http://www.db-thueringen.de/servlets/DocumentServlet?id=26272
Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Trunk, Carsten
The effect of finite rank perturbations on Jordan chains of linear operators. - In: Linear algebra and its applications, ISSN 0024-3795, Bd. 479 (2015), S. 118-130

http://dx.doi.org/10.1016/j.laa.2015.04.007
Azizov, Tomas Ya.; Trunk, Carsten
On a class of Sturm-Liouville operators which are connected to PT symmetric problems. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 14 (2014), 1, S. 991-992

http://dx.doi.org/10.1002/pamm.201410476
Huang, Junjie; Sun, Junfeng; Chen, Alatancang; Trunk, Carsten
The invertibility of 2 x 2 operator matrices. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 19 S., 305 KB). - (Preprint ; M14,10)

In this paper the properties of right invertible row operators, i.e., of 1x2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the invertibility of a 2x2 operator matrix. As an application, the invertibility of Hamiltonian operator matrices is investigated.



http://www.db-thueringen.de/servlets/DocumentServlet?id=25047
Jacob, Birgit; Langer, Matthias; Langer, Matthias *1972-*; Trunk, Carsten;
Variational principles for self-adjoint operator functions arising from second-order systems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 30 S., 455 KB). - (Preprint ; M14,09)
http://www.db-thueringen.de/servlets/DocumentServlet?id=25046
Philipp, Friedrich; Trunk, Carsten;
Spectral points of type π + and type π - of closed operators in indefinite inner product spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 27 S., 218 KB). - (Preprint ; M14,04)

We introduce the notion of spectral points of type π+ and type π- of closed operators A in a Hilbert space which is equipped with an indefinite inner product. It is shown that these points are stable under compact perturbations. In the second part of the paper we assume that A is symmetric with respect to the indefinite inner product and prove that the growth of the resolvent of A is of finite order in a neighborhood of a real spectral point of type π+ or π- which is not in the interior of the spectrum of A. Finally, we prove that there exists a local spectral function on intervals of type π+ or π-.



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