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Prof. Dr. Achim Ilchmann

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Ilchmann, Achim; Ke, Zhenqing; Logemann, Hartmut
Indirect sampled-data control with sampling period adaptation. - In: International journal of control. - London : Taylor & Francis, ISSN 1366-5820, Bd. 84 (2011), 2, S. 424-431

http://dx.doi.org/10.1080/00207179.2011.557782
Knobloch, Jürgen; Lloyd, David J. B.; Sandstede, Björn; Wagenknecht, Thomas
Isolas of 2-pulse solutions in homoclinic snaking scenarios. - In: Journal of dynamics and differential equations. - New York, NY [u.a.] : Springer Science + Business Media B.V., ISSN 1572-9222, Bd. 23 (2011), 1, S. 93-114

http://dx.doi.org/10.1007/s10884-010-9195-9
Hill, Adrian T.; Ilchmann, Achim
Exponential stability of time-varying linear systems. - In: IMA journal of numerical analysis : IMAJNA.. - Oxford : Oxford Univ. Press, ISSN 1464-3642, Bd. 31 (2011), 3, S. 865-885

http://www.dx.doi.org/10.1093/imanum/drq002
Philipp, Friedrich; Ran, André C. M.; ; ;
Local definitizability of T [*]T and TT[*]. - In: Integral equations and operator theory : IEOT.. - Berlin : Springer, ISSN 1420-8989, Bd. 71 (2011), 4, S. 491-508

http://dx.doi.org/10.1007/s00020-011-1913-0
Behrndt, Jussi; Möws, Roland; ; Trunk, Carsten;
Eigenvalue estimates for singular left-definite Sturm-Liouville operators. - In: Journal of spectral theory. - Zürich : EMS Publishing House, ISSN 1664-0403, Bd. 1 (2011), 3, S. 327-347

The spectral properties of a singular left-definite Sturm-Liouville operator $JA$ are investigated and described via the properties of the corresponding right-definite selfadjoint counterpart $A$ which is obtained by substituting the indefinite weight function by its absolute value. The spectrum of the $J$-selfadjoint operator $JA$ is real and it follows that an interval $(a,b)\subset\dR^+$ is a gap in the essential spectrum of $A$ if and only if both intervals $(-b,-a)$ and $(a,b)$ are gaps in the essential spectrum of the $J$-selfadjoint operator $JA$. As one of the main results it is shown that the number of eigenvalues of $JA$ in $(-b,-a) \cup (a,b)$ differs at most by three of the number of eigenvalues of $A$ in the gap $(a,b)$; as a byproduct results on the accumulation of eigenvalues of singular left-definite Sturm-Liouville operators are obtained. Furthermore, left-definite problems with symmetric and periodic coefficients are treated, and several examples are included to illustrate the general results.



https://doi.org/10.4171/JST/14
Philipp, Friedrich; Szafraniec, Franciszek Hugon; Trunk, Carsten;
Selfadjoint operators in S-spaces. - In: Journal of functional analysis. - Amsterdam [u.a.] : Elsevier, ISSN 1096-0783, Bd. 260 (2011), 4, S. 1045-1059

We study S-spaces and operators therein. An S-space is a Hilbert space with an additional inner product given by $\Skindef := (U\,\cdot\,,-)$, where $U$ is a unitary operator. We investigate spectral properties of selfadjoint operators in S-spaces. We show that their spectrum is symmetric with respect to the real axis. As a main result we prove that for each selfadjoint operator $A$ in an S-space we find an inner product which turns $\bez$ into a Krein space and $A$ into a selfadjoint operator therein. As a consequence we get a new simple condition for the existence of invariant subspaces of selfadjoint operators in Krein spaces, which provides a different insight into this well know and in general unsolved problem.



https://doi.org/10.1016/j.jfa.2010.10.023
Azizov, Tomas Ya.; Behrndt, Jussi; Jonas, Peter; Trunk, Carsten
Spectral points of definite type and type π for linear operators and relations in Krein spaces. - In: Journal of the London Mathematical Society. - Oxford : Wiley, ISSN 1469-7750, Bd. 83 (2011), 3, S. 768-788

Spectral points of positive and negative type, and type $\pi_{+}$ and type $\pi_{-}$ for closed linear operators and relations in Krein spaces are introduced with the help of approximative eigensequences. The main objective of the paper is to study these sign type properties in the non-selfadjoint case under various kinds of perturbations, e.g. compact perturbations and perturbations small in the gap metric. Many of the obtained perturbation results are also new for the special case of bounded and unbounded selfadjoint operators in Krein spaces.



http://dx.doi.org/10.1112/jlms/jdq098
Behrndt, Jussi; Hassi, Seppo; Snoo, Henk; Wietsma, Rudi; Winkler, Henrik
Linear fractional transformations of Stieltjes functions. - In: Proceedings in applied mathematics and mechanics : PAMM.. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 11 (2011), 1, S. 887-888

http://dx.doi.org/10.1002/pamm.201110430
Hennig, Eckhard; Krauße, Dominik; Schäfer, Eric; Sommer, Ralf; Trunk, Carsten; Winkler, Henrik
Frequency compensation for a class of DAE's arising in electrical circuits. - In: Proceedings in applied mathematics and mechanics : PAMM.. - Weinheim [u.a.] : Wiley-VCH, ISSN 1617-7061, Bd. 11 (2011), 1, S. 837-838

Structured perturbations of regular pencils of the form $sE-A$, $E,A\in\dR^{n\times n}, ˜s\in\dC,$ are considered which model the addition of a capacitance $c$ in an electrical circuit in order to improve the frequency response.



http://dx.doi.org/10.1002/pamm.201110407
Winkler, Henrik; Behrndt, Jussi; Hassi, Seppo; Snoo, Henk; Wietsma, Rudi
Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2011. - Online-Ressource (PDF-Datei: 26 S., 436,5 KB). . - (Preprint. - M11,18)
http://www.db-thueringen.de/servlets/DocumentServlet?id=19505