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Giribet, Juan; Langer, Matthias; Leben, Leslie; Maestripieri, Alejandra; Martínez Pería, Francisco; Trunk, Carsten;
Spectrum of J-frame operators - Ilmenau : Technische Universität, Institut für Mathematik, 2017 - 1 Online-Ressource (20 Seiten). . - (Preprint. - M17,01)

A J-frame is a frame F for a Krein space which is compatible with the indefinite inner product in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in H . With every J-frame the so-called J-frame operator is associated, which is a self-adjoint operator in the Krein space H. The J-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of J-frame operators in a Krein space by a 2X2 block operator representation. The J-frame bounds of F are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the 2X2 block representation. Moreover, this 2X2 block representation is utilized to obtain enclosures for the spectrum of J-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all J-frames associated with a given J-frame operator.



https://www.db-thueringen.de/receive/dbt_mods_00031058
Proch, Michael; Worthmann, Karl; Schlüchtermann, Jörg;
A negotiation-based algorithm to coordinate supplier development in decentralized supply chains. - In: European journal of operational research : EJOR. - Amsterdam [u.a.] : Elsevier, ISSN 0377-2217, Bd. 256 (2017), 2, S. 412-429

http://dx.doi.org/10.1016/j.ejor.2016.06.029
Behrndt, Jussi; Möws, Roland; Trunk, Carsten;
Eigenvalue estimates for operators with finitely many negative squares. - In: Opuscula mathematica : semiannual. - Kraków : AGH Univ. of Science and Technology Press, Bd. 36 (2016), 6, S. 717-734

http://dx.doi.org/10.7494/OpMath.2016.36.6.717
Braun, Philipp; Faulwasser, Timm; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl;
Maximal islanding time for microgrids via distributed predictive control. - In: 22nd International Symposium on Mathematical Theory of Networks and Systems : July 12-15, 2016, University of Minnesota, Twin Cities Campus. - Minneapolis, MN : University Digital Conservancy, ISBN 978-1-5323-1358-5, (2016), S. 652-659

http://hdl.handle.net/11299/181518
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl;
Model predictive control of residential energy systems using energy storage and controllable loads. - In: Progress in industrial mathematics at ECMI 2014 - Cham : Springer International Publishing, ISBN 978-3-319-23413-7, (2016), S. 617-623

https://doi.org/10.1007/978-3-319-23413-7_85
Shkalikov, A. A.; Trunk, Carsten;
On stability of closedness and self-adjointness for 2 x 2 operator matrices. - In: Mathematical notes - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 1573-8876, Bd. 100 (2016), 5, S. 870-875

http://dx.doi.org/10.1134/S0001434616110274
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl;
A distributed optimization algorithm for the predictive control of smart grids. - In: IEEE transactions on automatic control - New York, NY : Institute of Electrical and Electronics Engineers, ISSN 1558-2523, Bd. 61 (2016), 12, S. 3898-3911

https://doi.org/10.1109/TAC.2016.2525808
Jacob, Birgit; Langer, Matthias; Trunk, Carsten;
Variational principles for self-adjoint operator functions arising from second-order systems. - In: Operators and matrices : OaM. - Zagreb : Element, Bd. 10 (2016), 3, S. 501-531

http://dx.doi.org/10.7153/oam-10-29
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten;
Bounds on the non-real spectrum of a singular indefinite Sturm-Liouville operator on R. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 16 (2016), 1, S. 881-882

http://dx.doi.org/10.1002/pamm.201610429
Gernandt, Hannes; Trunk, Carsten;
On the parametric eigenvalue behavior of matrix pencils under rank one perturbations. - In: Proceedings in applied mathematics and mechanics : PAMM. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 16 (2016), 1, S. 873-874

http://dx.doi.org/10.1002/pamm.201610425