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Prof. Dr. Achim Ilchmann

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Leben, Leslie; Martínez Pería, Francisco; Philipp, Friedrich; Trunk, Carsten; Winkler, Henrik;
Finite rank perturbations of linear relations and singular matrix pencils. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (25 Seiten). . - (Preprint. - M18,08)

We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare the number of Jordan chains of length at least n corresponding to some eigenvalue to each other. In the operator case, it was recently proved that the difference of these numbers is independent of n and is at most the defect between the operators. One of the main results of this paper shows that in the case of linear relations this number has to be multiplied by n+1 and that this bound is sharp. The reason for this behaviour is the existence of singular chains. We apply our results to one-dimensional perturbations of singular and regular matrix pencils. This is done by representing matrix pencils via linear relations. This technique allows for both proving known results for regular pencils as well as new results for singular ones.
Gernandt, Hannes; Trunk, Carsten;
Locally finite extensions and Gesztesy-Šeba realizations for the Dirac operator on a metric graph. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (27 Seiten). . - (Preprint. - M18,07)

We study extensions of direct sums of symmetric operators S=\oplus S_n where n run through the natural numbers. In general there is no natural boundary triplet associated even if there is one for every S_n^*. We consider a subclass of extensions of S which can be described in terms of the boundary triplets of S_n^* and investigate the self-adjointness, the semi-boundedness from below and the discreteness of the spectrum. Sufficient conditions for these properties are obtained from recent results on weighted discrete Laplacians. The results are applied to Dirac operators on metric graphs with point interactions at the vertices. In particular, we allow graphs with arbitrarily small edge length.
Sprodowski, Tobias; Mehrez, Mohamed W.; Worthmann, Karl; Mann, George K. I.; Gosine, Raymond G.; Sagawa, Juliana K.; Pannek, Jürgen;
Differential communication with distributed MPC based on occupancy grid. - In: Information sciences : an international journal.. - New York, NY : Elsevier Science Inc., ISSN 0020-0255, Bd. 453 (2018), S. 426-441
Flaßkamp, Kathrin; Worthmann, Karl; Greiner-Petter, Christoph; Büskens, Christof; Sattel, Thomas;
An optimal control problem for stereotactic neurosurgery. - In: MATHMOD 2018 extended abstract volume : extended abstracts of 9th Vienna Conference on Mathematical Modelling, Vienna, Austria, February 21-23, 2018.. - Vienna : ARGESIM Publisher, ISBN 978-3-901608-91-9, (2018), S. 67-68
Ilchmann, Achim;
Das bürgerliche Stadthaus im Rokoko. - Tübingen : Wasmuth, 2018. - 255 Seiten. ISBN 3-8030-0833-6

Berger, Thomas; Gernandt, Hannes; Trunk, Carsten; Winkler, Henrik; Wojtylak, Michał;
The gap distance to the set of singular matrix pencils. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2018. - 1 Online-Ressource (22 Seiten). . - (Preprint. - M18,05)

We study matrix pencils sE-A using the associated linear subspace ker[A,-E]. The distance between subspaces is measured in terms of the gap metric. In particular, we investigate the gap distance of a regular matrix pencil to the set of singular pencils and provide upper and lower bounds for it. A relation to the distance to singularity in the Frobenius norm is provided.
Knobloch, Jürgen; Lamb, Jeroen S. W.; Webster, Kevin N.;
Shift dynamics near non-elementary T-points with real eigenvalues. - In: Journal of difference equations and applications. - London [u.a.] : Taylor & Francis, ISSN 1563-5120, Bd. 24 (2018), 4, S. 609-654
Hassi, Seppo; Snoo, Henk; Winkler, Henrik;
Limit properties of eigenvalues in spectral gaps. - In: Indefinite inner product spaces, Schur analysis, and differential equations : a volume dedicated to Heinz Langer.. - Cham : Birkhäuser, (2018), S. 335-355
Braun, Philipp; Faulwasser, Timm; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl;
Hierarchical distributed ADMM for predictive control with applications in power networks. - In: IFAC journal of systems and control. - Amsterdam : Elsevier Ltd., ISSN 2468-6018, Bd. 3 (2018), S. 10-22
Müller, Matthias A.; Worthmann, Karl;
On quadratic stage costs for mobile robots in model predictive control. - In: Proceedings in applied mathematics and mechanics : PAMM.. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 17 (2017), 1, S. 825-826