Publications Prof. Trunk

Publications of the employees

Publications of the Group

Results: 170
Created on: Thu, 28 Mar 2024 23:09:10 +0100 in 0.0757 sec


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.



http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2018200090
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.



http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2018200051
Bergmann, Jean Pierre; Bielenin, Martin; Herzog, Roland A.; Hildebrand, Jörg; Riedel, Ilka; Schricker, Klaus; Trunk, Carsten; Worthmann, Karl
Prevention of solidification cracking during pulsed laser beam welding. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 17 (2017), 1, S. 405-406

https://doi.org/10.1002/pamm.201710172
Berger, Thomas; Gernandt, Hannes; Trunk, Carsten; Winkler, Henrik; Wojtylak, Michał
A new bound for the distance to singularity of a regular matrix pencil. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 17 (2017), 1, S. 863-864

https://doi.org/10.1002/pamm.201710399
Gernandt, Hannes; Krauße, Dominik; Sommer, Ralf; Trunk, Carsten
A new method for network redesign via rank one updates. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 17 (2017), 1, S. 857-858

https://doi.org/10.1002/pamm.201710396
Behrndt, Jussi; Gsell, Bernhard; Schmitz, Philipp; Trunk, Carsten
An estimate on the non-real spectrum of a singular indefinite Sturm-Liouville operator. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 17 (2017), 1, S. 859-860

https://doi.org/10.1002/pamm.201710397
Derkach, Volodymyr; Trunk, Carsten
Coupling of definitizable operators in Kre&bovko;in spaces. - In: Nanosistemy: fizika, chimija, matematika, ISSN 2220-8054, Bd. 8 (2017), 2, S. 166-179

https://doi.org/10.17586/2220-8054-2017-8-2-166-179
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten
Spectral bounds for singular indefinite Sturm-Liouville operators with L1-potentials. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (7 Seiten). - (Preprint ; M17,12)Im Titel ist "1" hochgestellt

The spectrum of the singular indefinite Sturm-Liouville operator A=sgn(.) (-d^2/dx^2)+q with a real potential q in L^1(R)$ covers the whole real line and, in addition, non-real eigenvalues may appear if the potential q assumes negative values. A quantitative analysis of the non-real eigenvalues is a challenging problem, and so far only partial results in this direction were obtained. In this paper the bound l lambda | <= |q|_{L^1}^2 on the absolute values of the non-real eigenvalues lambda of A is obtained. Furthermore, separate bounds on the imaginary parts and absolute values of these eigenvalues are proved in terms of the L^1-norm of q and its negative part q_-.



http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2017200509
Behrndt, Jussi; Gsell, Bernhard; Schmitz, Philipp; Trunk, Carsten
An estimate on the non-real spectrum of a singular indefinite Sturm-Liouville operator. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (5 Seiten). - (Preprint ; M17,10)

It will be shown with the help of the Birman-Schwinger principle that the non-real spectrum of the singular indefinite Sturm-Liouville operator $\operatorname{sgn}(\cdot)(-\mathrm d^2/\mathrm d x^2 +q)$ with a real potential $q\in L^1\cap L^2$ is contained in a circle around the origin with radius $\|q\|_{L^1}^2$.



https://www.db-thueringen.de/receive/dbt_mods_00032787
Berger, Thomas; Gernandt, Hannes; Trunk, Carsten; Wojtylak, Michał
New lower bound for the distance to singularity of regular matrix pencils. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (5 Seiten). - (Preprint ; M17,10)

For regular matrix pencils $\Ac(s)=sE-A$ the distance to the nearest singular pencil in the Frobenius norm of the coefficients is called the distance to singularity. We derive a new lower bound for this distance by using the spectral theory of tridiagonal Toeplitz matrices.



https://www.db-thueringen.de/receive/dbt_mods_00032786