http://www.tu-ilmenau.de

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Arbeitsgruppe
Analysis und Systemtheorie

headerphoto Arbeitsgruppe Analysis und Systemtheorie
Ansprechpartner

Dr. Henrik Winkler

Privatdozent

Telefon +49 3677 69 3634

E-Mail senden

Ihre Position: 
INHALTE

Priv. Doz. Dr. Henrik Winkler

Priv.-Doz. Dr. rer. nat. habil. Henrik Winkler


Tel.: +49 3677 69-3634

Fax: +49 3677 69-3270

E-Mail: henrik.winkler@tu-ilmenau.de

Büro: Curiebau, Raum 231

Lehre

Lehrveranstaltungen im Sommersemester 2012

Vorlesungen:

Analysis 4: dienstags,  9:00 Uhr, Sr C 113

Übungen:

Mathematik 2 für Ingenieure: mittwochs, 17:00 Uhr, donnerstags, 11:00 Uhr, Sr K 2026

 

 


Forschung

- Structured perturbations of pencils related to electrical circuit design

- DAE's and structures of linear relations

- Spectral theory of systems of canonical differential equations, 

  indefinite vibrating strings, and Sturm-Liouville equations

- reproducing kernel Hilbert and Pontryagin spaces

- generalized Nevanlinna functions, asymptotic expansions

Publikationen

Refereed Journal Publications

  1. H. Winkler: Integral representations for stochastic processes with n-th stationary increments. Math. Nachr. 163 (1993), 35 - 44.

  2. H. Winkler: The inverse spectral problem for canonical systems. Integral Equations Oper. Theory 22 (1995), 360 - 374.

  3. H. Winkler: On transformations of canonical systems. Oper. Theory Adv. Appl. 80 (1995), 276 - 288.

  4. H. Langer, H. Winkler: Direct and inverse spectral problems for generalized strings. Integral Equations Oper. Theory 30 (1998), 409 - 431.

  5. H. Winkler: Canonical systems with a semibounded spectrum. Oper. Theory Adv. Appl. 106 (1998), 397 - 417.

  6. S. Hassi, H.S.V. de Snoo, H. Winkler: Boundary-value problems for twodimensional canonical systems. Integral Equations Oper. Theory 36 (2000), 445 - 479.

  7. H. Winkler: Spectral estimations for canonical systems. Math. Nachr. 220 (2000), 115 - 141.

  8. H. Winkler: Small perturbations of canonical systems. Integral Equations Oper. Theory 38 (2000), 222 - 250.

  9. H. Winkler: On generalized Friedrichs and Krein-von Neumann extensions and canonical systems. Math. Nachr. 236 (2002), 175 - 191.

  10. A. Sandovici, H.S.V. de Snoo, H. Winkler: The structure of linear relations in Euclidean spaces. Linear Algebra Appl. 397 (2005), 141 - 169.

  11. H.S.V. de Snoo, H. Winkler: Two-dimensional trace-normed canonical systems of di fferential equations and selfadjoint interface conditions. Integral Equations Oper. Theory 51 (2005), 73 - 108.

  12. H.S.V. de Snoo, H. Winkler: Canonical systems of di erential equations with selfadjoint interface conditions on graphs. Proc. Roy. Soc. Edinburgh 135 A (2005), 297 - 315.

  13. M. Kaltenbäck, H. Winkler, H. Woracek: Almost Pontryagin spaces. Oper. Theory Adv. Appl. 160 (2005), 253 - 271.

  14. M. Kaltenbäck, H. Winkler, H. Woracek: Symmetric relations of nite negatavity. Oper. Theory Adv. Appl. 162 (2005), 191 - 210.

  15. A. Fleige, S. Hassi, H.S.V. de Snoo, H. Winkler: Generalized Friedrichs extensions associated with interface conditions for Sturm - Liouville operators. Oper. Theory Adv. Appl. 163 (2005), 135 - 145.

  16. M. Kaltenbäck, H. Winkler, H.Woracek: Singularities of generalized strings. Oper. Theory Adv. Appl. 163 (2005), 191 - 248.

  17. M. Kaltenbäck, H. Winkler, H. Woracek: Generalized Nevanlinna functions with essentially positive spectrum. J. Oper. Theory 55 (1) (2006), 17 - 48.

  18. S. Hassi, A. Sandovici, H.S.V. de Snoo, H. Winkler: Form sums of nonnegative selfadjoint operators. Acta Math. Hungar. 111 (1-2) (2006), 81 - 105.

  19. S. Hassi, H.S.V. de Snoo, A.E. Sterk, H. Winkler: Non-standard boundary conditions for a class of Sturm-Liouville operators. Rev. Roumaine Math. Pures Appl. 51 (2006), 641 - 653.

  20. M. Kaltenbäck, H. Winkler: H. Woracek: De Branges spaces of entire functions symmetric about the origin. Integral Equations Oper. Theory 56 (2006), 483 - 509.

  21. S. Hassi, H.S.V. de Snoo, H. Winkler: On exceptional extensions close to the generalized Friedrichs extension of symmetric operators. Oper. Theory Adv. Appl. 175 (2007), 111 - 120.

  22. S. Hassi, H.S.V. de Snoo, A.E. Sterk, H. Winkler: Finite-dimensional graph perturbations of selfadjoint Sturm-Liouville operators. Operator Theory, Structured Matrices, and Dilations, Tiberiu Constantinescu Memorial Volume, Theta Series in Advanced Mathematics, (2007), 205 - 228.

  23. A. Sandovici, H.S.V. de Snoo, H. Winkler: Ascent, descent, nullity, defect, and related notions for linear relations in linear spaces. Linear Algebra Appl. 423 (2007) 456 - 497.

  24. M. Kaltenbäck, H. Winkler, H. Woracek: Strings, dual strings, and related canonical systems. Math. Nachr. 280 Nr. 13-14 (2007), 1518 - 1536.

  25. S. Hassi, A. Sandovici, H.S.V. de Snoo, H. Winkler: A general factorization approach to the extension theory of nonnegative operators and relations. J. Oper. Theory 58 (2) (2007) 351 - 386.

  26. S. Hassi, A. Sandovici, H.S.V. de Snoo, H. Winkler: Extremal extensions for the sum of nonnegative selfadjoint relations. Proc. Amer. Math. Soc. 135 (2007), 3193 - 3204.

  27. H. Winkler, H. Woracek: On semibounded canonical systems. Linear Algebra Appl. 429 (2008) 1082 - 1092.

  28. S. Hassi, A. Sandovici, H.S.V. de Snoo, H. Winkler: One-dimensional perturbations, asymptotic expansions, and spectral gaps. Oper. Theory Adv. Appl. 188 (2008), 149 - 173.

  29. A. Fleige, S. Hassi, H.S.V. de Snoo, H. Winkler: Sesquilinear forms corresponding to a non-semibounded Sturm-Liouville operator. Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), 291 - 318.

  30. J.-Ph. Labrousse, A. Sandovici, H.S.V. de Snoo, H. Winkler: The Kato decomposition for quasi - Fredholm relations. Operators and Matrices 4 (1), (2010), 1 - 51.


Further Publications, Proceedings

  1. H. Winkler: Generalized semi-martingale representations for processes with n-th stationary increments. Diploma thesis, 35 pp., TU Dresden, Germany, 1990.

  2. H. Winkler: On the inverse spectral problem for two-dimensional canonical systems. Doctoral dissertation, 61 pp., TU Vienna, Austria, 1993.

  3. H. Winkler: Spectral problems for canonical systems and generalized strings. Habilitation thesis, 163 pp., TU Dresden, Germany, 1999.

  4. H. Winkler: Spectral representations of canonical systems on a rami ed domain. Dresdener Schriften zur Mathematischen Stochastik, 3/2000 (preprint ISSN 0946-4735).

  5. H. Winkler: On exceptional extensions of symmetric relations with defect numbers (1; 1): Dresdener Schriften zur Mathematischen Stochastik 4/2000 (preprint ISSN 0946-4735).

  6. H. Winkler: Inverse problems for small perturbations of canonical systems. Proceedings of MTNS 2004, Leuven, Belgium, 3 pp., PaperID MSC-91.

  7. S. Hassi, A. Sandovici, H.S.V. de Snoo, H. Winkler: Extremal extensions of nonnegative linear relations. Proc. of the Algorithmic Information Theory Conference, Vaasa 2005, Finland, Vaasan Yliopiston Julkaisuja 124, (2005) 57 - 66.

  8. A. Sandovici, H.S.V. de Snoo, H. Winkler: Ascent, descent, nullity and defect for linear relations. Proceedings of the Algorithmic Information Theory Conference, Vaasa 2005, Finland, Vaasan Yliopiston Julkaisuja 124, (2005) 177 - 184.

  9. J.-Ph. Labrousse, A. Sandovici, H.S.V. de Snoo, H. Winkler: Quasi - Fredholm relations in Hilbert spaces. Universitatea din Bacau Studii si Cercetari Stiinti ce, Ser. Mat. 16, (2006) 93 -106.