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Prof. Dr. Achim Ilchmann

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Leben, Florian; Trunk, Carsten;
Operator-based approach to PT-symmetric problems on a wedge-shaped contour. - In: Quantum studies : mathematics and foundations. - Berlin : Springer, ISSN 2196-5617, Bd. 6 (2019), 3, S. 315-333

https://doi.org/10.1007/s40509-019-00197-3
Huang, Junjie; Sun, Junfeng; Chen, Alatancang; Trunk, Carsten;
Invertibility of 2 × 2 operator matrices. - In: Mathematische Nachrichten - [S.l.] : Wiley-VCH, ISSN 1522-2616, Bd. 292 (2019), 11, S. 2411-2426

https://doi.org/10.1002/mana.201800351
Campbell, Stephen L.; Ilchmann, Achim; Mehrmann, Volker; Reis, Timo
Applications of differential-algebraic equations: examples and benchmarks - Cham : Springer, 2019 - vii, 320 Seiten. . - (Differential-algebraic equations forum) ISBN 3-030-03717-7
Literaturangaben

Berger, Thomas; Giribet, Juan; Martínez Pería, Francisco; Trunk, Carsten;
On a class of non-Hermitian matrices with positive definite Schur complements. - In: Proceedings of the American Mathematical Society - Providence, RI : Soc., ISSN 1088-6826, Bd. 147 (2019), 6, S. 2375-2388

https://doi.org/10.1090/proc/14412
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten;
The non-real spectrum of a singular indefinite Sturm-Liouville operator with regular left endpoint - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019 - 1 Online-Ressource (3 Seiten). . - (Preprint. - M19,05)
https://www.db-thueringen.de/receive/dbt_mods_00038524
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten;
Spectral bounds for indefinite singular Sturm-Liouville operators with uniformly locally integrable potentials. - In: Journal of differential equations - Orlando, Fla. : Elsevier, ISSN 1090-2732, Bd. 267 (2019), 1, S. 468-493

https://doi.org/10.1016/j.jde.2019.01.013
Giribet, Juan; Langer, Matthias; Martínez Pería, Francisco; Philipp, Friedrich; Trunk, Carsten;
Spectral enclosures for a class of block operator matrices - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019 - 1 Online-Ressource (23 Seiten). . - (Preprint. - M19,04)

We prove new spectral enclosures for the non-real spectrum of a class of 2x2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators.



https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2019200198
Ilchmann, Achim; Leben, Leslie; Witschel, Jonas; Worthmann, Karl;
Optimal control of differential-algebraic equations from an ordinary differential equation perspective. - In: Optimal control, applications and methods - New York, NY [u.a.] : Wiley, ISSN 1099-1514, Bd. 40 (2019), 2, S. 351-366

https://doi.org/10.1002/oca.2481
Gernandt, Hannes; Pade, Jan Philipp;
Schur reduction of trees and extremal entries of the Fiedler vector. - In: Linear algebra and its applications : LAA. - New York, NY : American Elsevier Publ., Bd. 570 (2019), S. 93-122

https://doi.org/10.1016/j.laa.2019.02.008
Gernandt, Hannes; Moalla, Nedra; Philipp, Friedrich; Selmi, Wafa; Trunk, Carsten;
Invariance of the essential spectra of operator pencils - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019 - 1 Online-Ressource (15 Seiten). . - (Preprint. - M19,03)

The essential spectrum of operator pencils with bounded coefficients in a Hilbert space is studied. Sufficient conditions in terms of the operator coefficients of two pencils are derived which guarantee the same essential spectrum. This is done by exploiting a strong relation between an operator pencil and a specific linear subspace (linear relation).



https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2019200141