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Knobloch, Jürgen; Lamb, Jeroen S. W.; Webster, Kevin N.
Using Lin's method to solve Bykov's problems. - In: Journal of differential equations. - Orlando, Fla. : Elsevier, ISSN 1090-2732, Bd. 257 (2014), 8, S. 2984-3047
Snoo, Henk; deFleige, Andreas; Hassi, Seppo; Winkler, Henrik;
Non-semi-bounded closed symmetric forms associated with a generalized Friedrichs extension. - In: Proceedings. Mathematics / The Royal Society of Edinburgh. - Cambridge [u.a.] : Cambridge Univ. Press, 1943- , ISSN: 1473-7124 , ZDB-ID: 2036780-6, ISSN 1473-7124, Bd. 144 (2014), 4, S. 731-745
Reis, Timo; Selig, Tilman
Zero dynamics and root locus for a boundary controlled heat equation. - Hamburg : Fachbereich Mathematik, Univ. Hamburg, 2014. - Online-Ressource (PDF-Datei: 29 S., 229 KB). . - (Hamburger Beiträge zur Angewandten Mathematik. - 2014,08)
Worthmann, Karl; Damm, Tobias; Grüne, Lars; Stieler, Marleen
An exponential turnpike theorem for dissipative discrete time optimal control problems. - In: SIAM journal on control and optimization. - Philadelphia, Pa. : Soc., ISSN 1095-7138, Bd. 52 (2014), 3, S. 1935-1957
Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank
The role of sampling for stability and performance in unconstrained nonlinear model predictive control. - In: SIAM journal on control and optimization. - Philadelphia, Pa. : Soc., ISSN 1095-7138, Bd. 52 (2014), 1, S. 581-605
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.