Which point sets admit a k-angulation?. - In: Journal of computational geometry, ISSN 1920-180X, Bd. 5 (2014), 1, S. 41-55
http://www.db-thueringen.de/servlets/DocumentServlet?id=24187
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-.
http://www.db-thueringen.de/servlets/DocumentServlet?id=24132
Variable ordering structures in vector optimization. - Berlin : Springer, 2014. - xiii, 190 Seiten. - (Vector optimization) ISBN 978-3-642-54283-1
Description based upon print version of record
This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space. The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.
http://dx.doi.org/10.1007/978-3-642-54283-1
Die mathematische Zauberkiste : Mathematik für alle ; mathematische Knobeleien ; zeige mal, was du kannst!. - Ilmenau : Unicopy-Campus-Ed., 2014. - IV, 396 S.. - (Ilmenauer Editionen) ISBN 978-3-942646-03-1
Literaturverz. S. [393] - 396
Balancing transformations for infinite-dimensional systems with nuclear Hankel operator. - In: Integral equations and operator theory, ISSN 1420-8989, Bd. 79 (2014), 1, S. 67-105
http://dx.doi.org/10.1007/s00020-013-2105-x
Variation of discrete spectra of non-negative operators in Krein spaces. - In: Journal of operator theory, ISSN 1841-7744, Bd. 71 (2014), 1, S. 157-173
http://dx.doi.org/10.7900/jot.2011nov30.1964
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].
http://www.db-thueringen.de/servlets/DocumentServlet?id=24009
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.
http://www.db-thueringen.de/servlets/DocumentServlet?id=23864
On finite rank perturbations of selfadjoint operators in Krein spaces and eigenvalues in spectral gaps. - In: Complex analysis and operator theory, ISSN 1661-8262, Bd. 8 (2014), 4, S. 925-936
https://doi.org/10.1007/s11785-013-0318-2
An upper bound on the sum of powers of the degrees of simple 1-planar graphs. - In: Discrete applied mathematics, ISSN 1872-6771, Bd. 165 (2014), S. 146-151
https://doi.org/10.1016/j.dam.2012.11.001