Some Sobolev spaces as Pontryagin spaces. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2007. - 14 S. = 239,8 KB, Text. - (Preprint ; M07,17)
http://www.db-thueringen.de/servlets/DocumentServlet?id=9781
Prof. Dr. Carsten Trunk
Fachgebietsleiter
Anschrift:
Technische Universität Ilmenau
Fakultät für Mathematik und Naturwissenschaften
Institut für Mathematik
PF 10 05 65
98684 Ilmenau
Besuchsadresse:
Weimarer Straße 25
Curiebau, Zimmer C 226
98693 Ilmenau
Tel.: +49 3677 69-3253
Carsten Trunk mit H. Gernandt, The spectrum and the Weyr characteristics of operator pencils and linear relations,
Syphax Journal of Mathematics: Nonlinear Analysis, Operator and Systems 73 (2021), 73–89.
Carsten Trunk mit V. Derkach und P. Schmitz, PT -symmetric Hamiltonians as couplings of dual pairs, in
Contributions to Mathematics and Statistics: Essays in honor of Seppo Hassi (Hrsg. H.S.V de Snoo and
H.L. Wietsma), Acta Wasaensia 462 (2021), 55-68.
Carsten Trunk mit D.B. J. van Rensburg, M. van Straaten und F. Theron, Square roots of H-nonnegative matrices,
Linear Algebra Appl. 621 (2021), 29-49.
Branko Curgus, Volodymyr Derkach, Carsten Trunk,
Indefinite Sturm-Liouville operators in polar form,
submitted.
Thomas Berger, Henk de Snoo, Carsten Trunk, Henrik Winkler,
Linear relations and their singular chains,
submitted.
Janse van Rensburg, Madelein van Straaten, Frieda Theron, Carsten Trunk,
Square roots of H-nonnegative matrices,
to appear in Linear Algebra Appl.
Juan Giribet, Matthias Langer, Francisco Martinez Peria, Friedrich Philipp, and Carsten Trunk
Spectral enclosures for a class of block operator matrices;
J. Funct. Anal. 278 (2020).
Hannes Gernandt Nedra Moalla, Friedrich Philipp, Wafa Selmi, Carsten Trunk
Invariance of the essential spectra of operator pencils;
Oper. Theory Adv. Appl. 278 (2020), 203-219.
Florian Leben, Carsten Trunk
Operator based approach to PT-symmetric problems on a wedge-shaped contour;
Quantum Stud.: Math. Found. 6 (2019), 315-333. view online version
Junjie Huang, Junfeng Sun, Alatancang Chen, Carsten Trunk
The invertibility of 2x2 operator matrices; pdf-file
Math. Nachr. 292 (2019), 2411–2426.
Jussi Behrndt, Philipp Schmitz, Carsten Trunk,
Spectral bounds for indefinite singular Sturm-Liouville operators with uniformly locally integrable potentials;
J. Differential Equations 267 (2019), 468-493.
Thomas Berger, Juan Giribet, Francisco Martinez Peria und Carsten Trunk
On a class of non-Hermitian matrices with positive definite Schur complements;
Proc. Amer. Math. Soc. 147 (2019), 2375-2388.
Leslie Leben, Francisco Martinez Peria, Friedrich Philipp, Carsten Trunk and Henrik Winkler
Finite rank perturbations of linear relations and singular matrix pencils;
Complex Anal. Oper. Theory, DOI: doi.org/10.1007/s11785-021-01082-x
Hannes Gernandt, and Carsten Trunk
Locally finite extensions and Gesztesy-Seba realizations for the Dirac operator on a metric graph
submitted.
Thomas Berger, Hannes Gernandt, Carsten Trunk, Henrik Winkler, and Michał Wojtylak
The gap distance to the set of singular matrix pencils,
Linear Algebra Appl. 564 (2019), 28-57.
Jussi Behrndt, Philipp Schmitz, Carsten Trunk,
Spectral bounds for singular indefinite Sturm-Liouville operators with L^1-potentials;
Proc. Amer. Math. Soc. 146 (2018), 3935-3942;
Birgit Jacob, Christiane Tretter, Carsten Trunk, Hendrik Vogt,
Systems with strong damping and their spectra;
Math. Methods Appl. Sci. 41 (2018), 6546-6573.
Juan Giribet, Matthias Langer, Leslie Leben, Alejandra Maestripieri, Francisco Martinez Peria, Carsten Trunk
Spectrum of J-frame Operators, Opusc. Math. 38 (2018) 623-649;
Vladimir Derkach, Carsten Trunk,
Coupling of Definitizable Operators in Krein Spaces;
NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS 8 (2017) 166–179;
Andrei .A. Shkalikov, C. Trunk
On stability of closeness and self-adjointness for 2x2 operator matrices,
Math. Notes 100 (2016), 870-875;
Jussi Behrndt, Roland Möws, Carsten Trunk
Eigenvalue estimates for operators with finitely many negative squares; pdf-file
Opusc. Math. 36 (2016), 717-734;
Hannes Gernandt, Carsten Trunk
Eigenvalue placement for regular matrix pencils with rank one perturbations; pdf-file
SIAM. J. Matrix Anal. Appl. 38 (2017), 134-154 http://dx.doi.org/10.1137/16M1066877;
Thomas Berger, Carsten Trunk, Henrik Winkler
Linear relations and the Kronecker canonical form; pdf-file
Linear Algebra Appl. 488 (2016), 13-44;
Birgit Jacob, Matthias Langer, Carsten Trunk
Variational principles for self-adjoint operator functions arising from second-order systems; pdf-file
Operators and Matrices 10 (2016), 501-531;
Jussi Behrndt, Leslie Leben, Francisco Martinez Peria, Carsten Trunk
The effect of finite rank perturbations on Jordan chains of linear operators;pdf-file
Linear Algebra Appl. Vol. 479 (2015), 118-130;
Achim Ilchmann, Tilman Selig, Carsten Trunk
The Byrnes-Isidori form for infinite-dimensional systems; pdf-file
SIAM J. on Control Optim. Vol. 54 (2016), 1504-1534;
Jussi Behrndt, Leslie Leben, Francisco Martinez Peria, Roland Möws, Carsten Trunk
Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces; [pdf-file]
J. Math. Anal. Appl. Vol. 439 (2016), 864-895;
Friedrich Philipp, Carsten Trunk
Spectral points of type pi_+ and type pi_- of closed operators in indefinite inner product spaces; [pdf-file]
Operators and Matrices Vol. 9 (2015), 481-506;
Jussi Behrndt, Roland Möws, Carsten Trunk
On finite Rank Perturbations of Selfadjoint Operators in Krein Spaces and Eigenvalues in Spectral Gaps;[pdf-file]
Complex Anal. Oper. Theory Vol. 8 (2013), 925-936;
Jussi Behrndt, Friedrich Philipp, Carsten Trunk
Bounds on the non-real spectrum of differential operators with indefinite weights;[pdf-file]
Math. Ann. Vol. 357 (2013), 185-213;
Jussi Behrndt, Annemarie Luger, Carsten Trunk
On the negative squares of a class of self-adjoint extensions in Krein spaces; [pdf-file]
Math. Nachr. Vol. 286 (2013), 118-148;
Friedrich Philipp, Carsten Trunk
The numerical range of non-negative operators in Krein spaces;[pdf-file]
Linear Algebra Appl. Vol. 438 (2013), 2542–2556;
Friedrich Philipp, Vladimir Strauss, Carsten Trunk
Local spectral theory for normal operators in Krein spaces; [pdf-file]
Math. Nachr. Vol. 286 (2013), 32-58;
Tomas Azizov, Carsten Trunk
PT Symmetric, Hermitian and P-Self-Adjoint operators related to potentials in PT Quantum Mechanics; [pdf-file]
J. Math. Phys. Vol. 53 (2012), 012109;
Jussi Behrndt, Roland Möws, Carsten Trunk
Eigenvalue estimates for singular left-definite Sturm-Liouville operators; [pdf-file]
J. Spectr. Theory Vol. 1 (2011), 327-347;
Sergii Kuzhel, Carsten Trunk
On a class of J-self-adjoint operators with empty resolvent set; [pdf-file]
J. Math. Anal. Appl. Vol. 379 (2011), 272–289;
Friedrich Philipp, Franciszek Hugon Szafraniec, Carsten Trunk
Selfadjoint operators in S-Spaces; [pdf-file]
J. Funct. Anal. Vol. 260 (2011), 1045-1059;
Tomas Azizov, Jussi Behrndt, Peter Jonas, Carsten Trunk
Spectral points of definite type and type pi for linear operators and relations in Krein spaces; [pdf-file]
J. London Math. Soc. Vol. 83 (2011), 768-–788.
Tomas Azizov, Peter Jonas, Carsten Trunk
Small perturbation of selfadjoint and unitary operators in Krein spaces; [pdf-file]
J. Operator Theory Vol. 64 (2010), 401-416;
Tomas Azizov, Carsten Trunk
On domains of PT Symmetric operators related to -y''(x) + (-1)^n x^{2n}y(x); [pdf-file]
J. Phys. A: Math. Theor. Vol. 43 (2010), 175303
Mark-Alexander Henn, Christian Mehl, Carsten Trunk
Hyponormal and strongly Hyponormal matrices in Inner Product Spaces;
Linear Algebra Appl. Vol. 433 (2010), 1055-1076; [pdf-file]
Carsten Trunk
Analyticity of semigroups related to a class of block operator matrices; [pdf-file]
Operator Theory: Advances and Applications Vol. 195 (2009), 257-271.
Jussi Behrndt, Qutaibeh Katatbeh, Carsten Trunk
Non-Real eigenvalues of singular indefinite Sturm-Liouville operators;
Proc. Amer. Math. Soc. Vol. 137 (2009), 3797-3806; [pdf-file]
Birgit Jacob, Carsten Trunk
Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics; [pdf-file]
Semigroup Forum Vol. 79 (2009), 79-100.
Friedrich Philipp, Carsten Trunk
G-Selfadjoint operators in Almost Pontryagin spaces; [pdf-file]
Operator Theory: Advances and Applications Vol. 188 (2009) 207-236.
Tomas Azizov, Jussi Behrndt, Peter Jonas, Carsten Trunk
Compact and finite rank perturbations of linear relations in Hilbert spaces; [pdf-file]
Integral Equations Operator Theory Vol. 63 (2009) 151-163.
Tomas Azizov, Jussi Behrndt, Friedrich Philipp, Carsten Trunk
On domains of powers of linear operators and finite rank perturbations; [pdf-file]
Operator Theory: Advances and Applications Vol. 188 (2009), 31-36.
Illya Karabash, Carsten Trunk
Spectral properties of singular Sturm-Liouville operators; [pdf-file]
Proc. R. Soc. Edinb. Sect. A. Vol. 139 (2009), 483-503.
Vladimir Strauss, Carsten Trunk
Spectralizable operators; [pdf-file]
Integral Equations Operator Theory Vol. 61 (2008) 413-422.
Jussi Behrndt, Qutaibeh Katatbeh, Carsten Trunk
Accumulation of complex eigenvalues of indefinite Sturm-Liouville operators; [pdf-file]
J. Phys. A: Math. Theor. Vol. 41 (2008) 244003.
Birgit Jacob, Carsten Trunk, Monika Winklmeier
Analyticity and Riesz basis property of semigroups associated to damped vibrations;
Journal of Evolution Equations Vol. 8 (2008), 263-281.
Carsten Trunk
Spectral theory for operator matrices related to models in mechanics;
Math. Notes, Vol. 83 (2008), 843-850.
Tomas Azizov, Jussi Behrndt, Carsten Trunk
On finite rank perturbations of definitizable operators;
J. Math. Anal. Appl. Vol. 339 (2008), 1161-1168.
Birgit Jacob, Kirsten Morris, Carsten Trunk
Minimum-Phase infinite-dimensional second-order systems;
IEEE Transactions on Automatic Control Vol. 52 (2007), 1654-1665.
Peter Jonas, Carsten Trunk
A Sturm-Liouville problem depending rationally on the eigenvalue parameter;
Math. Nachr. Vol. 280 (2007), 1709-1726.
Jussi Behrndt, Carsten Trunk
On the negative squares of indefinite Sturm-Liouville operators;
J. Differential Equations, Vol. 238 (2007), 491-519;
Birgit Jacob, Carsten Trunk
Location of the spectrum of operator matrices which are associated to second order equations;
Operators and Matrices, Vol. 1 (2007), 45-60;
Christian Mehl, Carsten Trunk
The adjoint of matrices in degenerate indefinite inner product spaces;
Operator Theory: Advances and Applications Vol. 175 (2007), 193-209;
Jussi Behrndt, Annemarie Luger, Carsten Trunk
Generalized resolvents of a class of symmetric operators in Krein spaces.
Operator Theory: Advances and Applications Vol. 175 (2007), 13-33;
Jussi Behrndt, Friedrich Philipp, Carsten Trunk
Properties of the spectrum of type pi+ and type pi- of self-adjoint operators in Krein spaces;
Methods Funct. Anal. Topology Vol. 12 (2006), 326-340;
Jussi Behrndt, Carsten Trunk
Sturm-Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions;
J. Differential Equations Vol. 222 (2006), 297-324;
Tomas Ya. Azizov, Peter Jonas, Carsten Trunk
Spectral points of type $pi_{+}$ and $pi_{-}$ of self-adjoint operators in Krein spaces.
J. Funct. Anal. Vol. 226 (2005), 114-137;
Peter Jonas, Carsten Trunk
On a class of analytic operator functions and their linearizations.
Math. Nachr. Vol. 243 (2002), 92-133.
Jussi Behrndt, Philipp Schmitz, Carsten Trunk
The non-real spectrum of a singular indefinite Sturm–Liouville operator with regular left endpoint
submitted to Proc. Appl. Math. Mech.; pdf-file
Jussi Behrndt, Bernhard Gsell, Philipp Schmitz, Carsten Trunk
An estimate on the non-real spectrum of a singular indefinite Sturm-Liouville operator,
Proc. Appl. Math. Mech. 17 (2017), 859-860; pdf-file
Thomas Berger, Hannes Gernandt, Carsten Trunk, Henrik Winkler, Michal Wojtylak
A New bound for the distance to singularity of a regular matrix pencil,
Proc. Appl. Math. Mech. 17 (2017), 863-864; pdf-file
Jean Pierre Bergmann, Martin Bielenin, Roland Herzog, Jörg Hildebrand, Ilka Riedel, Klaus Schricker, Carsten Trunk, Karl Worthmann
Prevention of solidification cracking during pulsed laser beam welding,
Proc. Appl. Math. Mech. 17 (2017), 405-406; pdf-file
Hannes Gernandt, Dominik Krauße, Carsten Trunk, Ralf Sommer
A new method for network redesign via rank one updates,
Proc. Appl. Math. Mech. 17 (2017), 857-858; pdf-file
Jussi Behrndt, Philipp Schmitz, Carsten Trunk
Bounds on the Non-real Spectrum of a Singular Indefinite Sturm-Liouville Operator on R.
Proc. Appl. Math. Mech. 16 (2016), 881–882; pdf-file
Hannes Gernandt, Carsten Trunk
On the parametric eigenvalue behavior of matrix pencils under rank one perturbations.
Proc. Appl. Math. Mech. 16 (2016), 877–874; pdf-file
Florian Büttner, Carsten Trunk
Limit-point / limit-circle classification of second-order differential operators arising in PT quantum mechanics.
Proc. Appl. Math. Mech. 16 (2016), 871–872; pdf-file
Carsten Trunk,
Eigenvalue estimates for operators with finitely many negative squares.
Oberwolfach Reports 12 (2015), 17-20; [pdf-file]
Tomas Azizov, Carsten Trunk
On a class of Sturm-Liouville operators which are connected to PT symmetric problems.
Proc. Appl. Math. Mech. 14 (2014), 991–992; [pdf-file]
Carsten Trunk
Locally definitizable operators: The local structure of the spectrum.
in: Operator Theory, D. Alpay (Ed.), pg. 241-259. Springer 2015; [pdf-file]
Vladimir Strauss, Carsten Trunk
Some Sobolev spaces as Pontryagin spaces.
Vestnik SUSU. Series Mathematics, Mechanics, Physics 6, No. 11 (270), 14-23 (2012); [pdf-file]
Eckhard Hennig, Dominik Krauße, Eric Schäfer, Ralf Sommer, Carsten Trunk, Henrik Winkler
Frequency compensation for a class of DAE's arising in electrical circuits.
Proc. Appl. Math. Mech. 11 (2011), 837-838; [pdf-file]
Jussi Behrndt, Friedrich Philipp, Carsten Trunk
Definitizability of a Class of J-Selfadjoint Operators with Applications.
Proc. Appl. Math. Mech. 9 (2009), 665-666; [pdf-file]
Jussi Behrndt, Roland Möws, Carsten Trunk
Singular Indefinite Sturm-Liouville Operators with a Spectral Gap.
Proc. Appl. Math. Mech. 9 (2009), 669-670; [pdf-file]
Birgit Jacob, Carsten Trunk
On the spectrum and analyticity of semigroups associated to second-order systems.
Proceedings 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Blacksburg, USA, (2008); [pdf-file]
Birgit Jacob, Carsten Trunk
Block operator matrices and second-order systems.
Proceedings 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, (2006); [pdf-file]
Birgit Jacob, Kirsten Morris, Carsten Trunk
Minimum-Phase behaviour of damped second-order systems with position measurements.
Proceedings 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, (2006); [pdf-file]
Birgit Jacob, Kirsten Morris, Carsten Trunk
Minimum-Phase second-order systems and the spectrum of the semigroup generator.
Proc. Appl. Math. Mech. 6 (2006), 631-632; [pdf-file]
Jussi Behrndt, Carsten Trunk
On generalized resolvents of symmetric operators of defect one with finitely many negative squares.
Proceedings AIT Conference, Vaasan Yliop. Julk. Selvityksiä Rap. 124, Vaasa, Finland (2005), 21-30; [pdf-file]
Carsten Trunk
Spectral Theory for Second Order Systems and Indefinite Sturm-Liouville Problems,
Habilitation, Technische Universität Ilmenau (2010); [pdf-file]
Carsten Trunk
Spectral Properties of a Class of Analytic Operator Functions and Their Linearizations.
Dissertation, Technische Universität Berlin (2002); [pdf-file]
Carsten Trunk
Über eine Klasse von Differentialoperatoren zweiter Ordnung, die nichtlinear vom Eigenwertparameter abhängen.
Diplomarbeit, Technische Universität Berlin (1995); [pdf-file]
Gut vorbereitet in die erste Mathematikklausur,
Klausurtraining für Studierende an Universitäten und Fachhochschulen
Etienne Emmrich, Carsten Trunk, 06/2020, 240 p., Carl Hanser Verlag Leipzig, 2. Auflage.
GAMM-Mitteilungen
Volume 41, Issue 4
Surveys for Applied Mathematics and Mechanics; Editor: A. Menzel, Dortmund; Managing Editor: R. Ostwald, Dortmund; Topical Issue: Applied Operator Theory – Part II; Guest Editors: B. Jacob, Wuppertal; J. Behrndt, Graz; C. Tretter, Bern; C. Trunk, Ilmenau; WILEY, November 2018
GAMM-Mitteilungen
Volume 41, Issue 3
Surveys for Applied Mathematics and Mechanics; Editor: A. Menzel, Dortmund; Managing Editor: R. Ostwald, Dortmund; Topical Issue: Applied Operator Theory – Part I; Guest Editors: B. Jacob, Wuppertal; J. Behrndt, Graz; C. Tretter, Bern; C. Trunk, Ilmenau; WILEY, September 2018
Proceedings in Applied Mathematics and Mechanics Volume 17, 2017
Volume 17, Issue 1
Special Issue: 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017; Editors: C. Könke, Weimar, and C. Trunk, Ilmenau
Pages: 1-876, WILEY, December 2017
Recent Advances in Operator Theory in Hilbert and Krein Spaces,
in Operator Theory: Advances and Applications, Vol. 198,
J. Behrndt, K.-H. Förster, C. Trunk (Eds.), 2010, 324 p., Birkhäuser Verlag Basel.
Spectral Theory in Inner Product Spaces and Applications,
in Operator Theory: Advances and Applications, Vol. 188,
J. Behrndt, K.-H. Förster, H. Langer, C. Trunk (Eds.), 2009, 268 p., Birkhäuser Verlag Basel.
Gut vorbereitet in die erste Mathe-Klausur,
Klausurtraining für Studierende an Universitäten und Fachhochschulen
Etienne Emmrich, Carsten Trunk, 2007, 240 p., Carl Hanser Verlag Leipzig.
Operator Theory in Inner Product Spaces,
in Operator Theory: Advances and Applications, Vol. 175,
K.-H. Förster, P. Jonas, H. Langer, C. Trunk (Eds.), 2007, 255 p., Birkhäuser Verlag Basel.
J. Behrndt, P. Schmitz, C. Trunk, Spectral bounds for indefinite singular Sturm–Liouville operators with uniformly locally integrable potentials. J. Differ. Equations 267 (2019), 468–493. Preprint
J. Behrndt, P. Schmitz, C. Trunk, Spectral bounds for singular indefinite Sturm–Liouville operators with L1 -potentials. Proc. Am. Math. Soc. 146 (2018), 3935–3942. Preprint
J. Behrndt, P. Schmitz, C. Trunk, The non‐real spectrum of a singular indefinite Sturm–Liouville operator with regular left endpoint, Proc. appl. Math. Mech. 19 (2019). Preprint
J. Behrndt, B. Gsell, P. Schmitz, C. Trunk, An estimate on the non-real spectrum of a singular indefinite Sturm–Liouville operator, Proc. appl. Math. Mech. 17 (2017), 859–860. Preprint
J. Behrndt, P. Schmitz, C. Trunk, Bounds on the non-real spectrum of a singular indefinite Sturm–Liouville operator on R, Proc. appl. Math. Mech. 16 (2016), 881–882. Preprint
P. Schmitz, Zur WKB-Näherung für Lösungen gewöhnlicher Differentialgleichungen einer komplexen Veränderlichen. Masterarbeit
P. Schmitz, Zur Selbstadjungiertheit regulärer Sturm-Liouville-Differentialoperatoren. Bachelorarbeit