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Philipp, Friedrich; Trunk, Carsten
Spectral points of type π + and type π - of closed operators in indefinite inner product spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 27 S., 218 KB). . - (Preprint. - M14,04)

We introduce the notion of spectral points of type π+ and type π- of closed operators A in a Hilbert space which is equipped with an indefinite inner product. It is shown that these points are stable under compact perturbations. In the second part of the paper we assume that A is symmetric with respect to the indefinite inner product and prove that the growth of the resolvent of A is of finite order in a neighborhood of a real spectral point of type π+ or π- which is not in the interior of the spectrum of A. Finally, we prove that there exists a local spectral function on intervals of type π+ or π-.
Reis, Timo; Selig, Tilman
Balancing transformations for infinite-dimensional systems with nuclear Hankel operator. - In: Integral equations and operator theory : IEOT.. - Berlin : Springer, ISSN 1420-8989, Bd. 79 (2014), 1, S. 67-105
Behrndt, Jussi; Leben, Leslie; Philipp, Friedrich
Variation of discrete spectra of non-negative operators in Krein spaces. - In: Journal of operator theory. - Bucharest, ISSN 1841-7744, Bd. 71 (2014), 1, S. 157-173
Azizov, Tomas Ya.; Trunk, Carsten
On limit point and limit circle classification for PT symmetric operators. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 5 S., 103,3 KB). . - (Preprint. - M14,03)

A prominent class of PT-symmetric Hamiltonians is $H:= 1/2 p^2 + x^2 (ix)^N, for x \in \Gamma$ for some nonnegative number N. The associated eigenvalue problem is defined on a contour $\Gamma$ in a specific area in the complex plane (Stokes wedges), see [3,5]. In this short note we consider the case N=2 only. Here we elaborate the relationship between Stokes lines and Stokes wedges and well-known limit point/limit circle criteria from [11, 6, 10].
Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Trunk, Carsten
The effect of finite rank perturbations on Jordan chains of linear operators. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 12 S., 280,7 KB). . - (Preprint. - M14,02)

A general result on the structure and dimension of the root subspaces of a matrix or a linear operator under finite rank perturbations is proved: The increase of dimension from the n-th power of the kernel of the perturbed operator to the (n+1)-th power differs from the increase of dimension of the corresponding powers of the kernels of the unperturbed operator by at most the rank of the perturbation and this bound is sharp.
Behrndt, Jussi; Möws, Roland; Trunk, Carsten
On finite rank perturbations of selfadjoint operators in Krein spaces and eigenvalues in spectral gaps. - In: Complex analysis and operator theory. - Cham (ZG) : Springer International Publishing AG, ISSN 1661-8262, Bd. 8 (2014), 4, S. 925-936
Snoo, Henk; deWinkler, Henrik; Wojtylak, Michal
Global and local behavior of zeros of nonpositive type. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, ISSN 1096-0813, Bd. 414 (2014), 1, S. 273-284
Pannek, Jürgen; Worthmann, Karl
Stability and performance guarantees for model predictive control algorithms without terminal constraints. - In: ZAMM : journal of applied mathematics and mechanics.. - Berlin : Wiley-VCH, ISSN 1521-4001, Bd. 94 (2014), 4, S. 317-330
Homburg, Ale Jan; Kellner, Maria; Knobloch, Jürgen
Construction of codimension one homoclinic cycles. - In: Dynamical systems : an international journal.. - London : Taylor & Francis, ISSN 1468-9375, Bd. 29 (2014), 1, S. 133-151
Grüne, Lars; Allgöwer, Frank; Findeisen, Rolf; Fischer, Jörg; Groß, Dominik; Hanebeck, Uwe D.; Kern, Benjamin; Müller, Matthias A.; Pannek, Jürgen; Reble, Marcus
Distributed and networked model predictive control. - In: Control theory of digitally networked dynamic systems. - Cham : Springer, (2014), S. 111-167