On a class of non-Hermitian matrices with positive definite Schur complements. - In: Proceedings of the American Mathematical Society, ISSN 1088-6826, Bd. 147 (2019), 6, S. 2375-2388
https://doi.org/10.1090/proc/14412
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
Spectral bounds for indefinite singular Sturm-Liouville operators with uniformly locally integrable potentials. - In: Journal of differential equations, ISSN 1090-2732, Bd. 267 (2019), 1, S. 468-493
https://doi.org/10.1016/j.jde.2019.01.013
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
Schur reduction of trees and extremal entries of the Fiedler vector. - In: Linear algebra and its applications, ISSN 0024-3795, Bd. 570 (2019), S. 93-122
https://doi.org/10.1016/j.laa.2019.02.008
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
Operator based approach to PT-symmetric problems on a wedge-shaped contour. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019. - 1 Online-Ressource (23 Seiten). - (Preprint ; M19,02)
We consider a second-order differential equation -y''(z)-(iz)^{N+2}y(z)=\lambda y(z), z\in \Gamma with an eigenvalue parameter \lambda \in C. In PT quantum mechanics z runs through a complex contour \Gamma in C, which is in general not the real line nor a real half-line. Via a parametrization we map the problem back to the real line and obtain two differential equations on [0,\infty) and on (-\infty,0]. They are coupled in zero by boundary conditions and their potentials are not real-valued. The main result is a classification of this problem along the well-known limit-point/ limit-circle scheme for complex potentials introduced by A.R. Sims 60 years ago. Moreover, we associate operators to the two half-line problems and to the full axis problem and study their spectra.
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2019200020
Spectral bounds for indefinite singular Sturm-Liouville operators with uniformly locally integrable potentials. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019. - 1 Online-Ressource (26 Seiten). - (Preprint ; M19,01)
The non-real spectrum of a singular indefinite Sturm-Liouville operator A=1/r (-d/dx p d/dx+q) with a sign changing weight function r consists (under suitable additional assumptions on the real coefficients 1/p,q,r in L^1_loc(R)) of isolated eigenvalues with finite algebraic multiplicity which are symmetric with respect to the real line. In this paper bounds on the absolute values and the imaginary parts of the non-real eigenvalues of A are proved for uniformly locally integrable potentials q and potentials $q in L^s(R) for some s in [1,\infty]. The bounds depend on the negative part of q, on the norm of 1/p and in an implicit way on the sign changes and zeros of the weight function.
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2019200016
The gap distance to the set of singular matrix pencils. - In: Linear algebra and its applications, ISSN 0024-3795, Bd. 564 (2019), S. 28-57
https://doi.org/10.1016/j.laa.2018.11.020
Systems with strong damping and their spectra. - In: Mathematical methods in the applied sciences, ISSN 1099-1476, Bd. 41 (2018), 16, S. 6546-6573
https://doi.org/10.1002/mma.5166