Home Page of Helge Krüger

Picture courtesy of Evelyn Lamb.

Address: Helge Krüger
Department of Mathematics-- MS 136, Rice University
6100 S. Main St., Houston TX 77005-1892
USA

Office: Herman Brown Hall 42

Email: helge.krueger@rice.edu.

I am currently graduate student at Rice University supervised by David Damanik. I have obtained my master degree at the University of Vienna under Gerald Teschl.

I am interested in the spectral theory of discrete one-dimensional Schrödinger operators. In particular of the Lyapunov exponent and the essential spectrum. Furthermore, I am interested in the Toda lattice and Oscillation Theory.

More information on my research can be found in my Research Statement.

Upcoming Events

November 23 - 29: Universidad Nacional Autonoma de Mexico, Mexico City.
January 13 - 16, 2010: Joint Mathematics Meetings, San Fransisco.
March 27 - 28, 2010: AMS Southeastern Sectional Meeting, Lexington, Kentucky.
Mai 15 - September 15, 2010: Erwin Schrödinger Institute, Vienna, Austria.
Mai 25 - 28, 2010: AIMS 2010, Dresden, Germany.

Preprints

Optimality of log Hölder continuity of the integrated density of states, with Z. Gan, [TeX | DVI | PDF].
Multiscale Analysis for Ergodic Schrödinger operators and positivity of Lyapunov exponents. [TeX | DVI | PDF].
Probabilistic averages of Jacobi operators. [TeX | DVI | PDF].
Unique continuation for discrete nonlinear wave equations, with G. Teschl. [TeX | DVI | PDF].
On Perturbations of Quasi-Periodic Schrödinger operators, [TeX | DVI | PDF].

Publications

A family of Schrödinger Operators whose spectrum is an interval , Comm. Math. Phys. 290:3, 935-939 (2009). [TeX | DVI | PDF].
Schrödinger Operators defined by Interval Exchange Transformations , with J. Chaika and D. Damanik, J. Mod. Dyn. 3:2, 253-270 (2009), [TeX | DVI | PDF].
Stability of the Periodic Toda Lattice in the Soliton Region, with G. Teschl, Int. Math. Res. Not. 2009, Art. ID rnp077, 36pp (2009). [TeX | DVI | PDF].
Long-Time Asymptotics of the Toda Lattice for Decaying Initial Data Revisited, with G. Teschl, Rev. Math. Phys. 21:1, 61-109 (2009). [TeX | DVI | PDF].
Almost Periodic Szegö Cocycles with Uniformly Positive Lyapunov Exponents, with D. Damanik, J. Approx. Theory (to appear). [TeX | DVI | PDF].
Long-Time Asymptotics for the Toda Lattice in the Soliton Region, with G.Teschl, Math. Z. 262, 585-602 (2009), [TeX | DVI | PDF].
Effective Prüfer Angles and Relative Oscillation Criteria, with G. Teschl, J. Diff. Eq. 245, 3823-3848 (2008), [TeX | DVI | PDF].
Relative Oscillation Theory for Sturm--Liouville operators extended, with G. Teschl, J. Funct. Anal. 254:6, 1702-1720 (2008), [TeX | DVI | PDF].
Relative Oscillation Theory, weighted Zeros of the Wronskian, and the Spectral Shift Function, with G. Teschl, Comm. Math. Phys. 287:2, 613-640 (2009). [TeX | DVI | PDF].

All publications and preprints are also available at the arxiv, ZMATH and MathSciNet.

Thesis

Relative Oscillation Theory for Sturm-Liouville operators, Master Thesis, University of Vienna, December 2006. [TeX | PDF]

Helge Krüger, 2009.