Publikationen Prof. Trunk

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Results: 171
Created on: Wed, 24 Apr 2024 23:09:49 +0200 in 0.0720 sec
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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.



    https://www.db-thueringen.de/receive/dbt_mods_00034936
    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

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