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Publications and Preprints

     

  • Aperiodic order and pure point diffraction, to appear in: The Philosophical Magazine (0802.324)

  • Eigenfunction expansion for Schrodinger operators on metric graphs (with Carsten Schubert, Peter Stollmann), to appear in: Integral Equations and Operator Theory, (0801.1376)

  • Uniform existence of the integrated density of states for combinatorial and metric graphs over Z^d (with Michael Gruber, Ivan Veselic), in: Analysis on Graphs and its Applications (edited by P. Exner, J. Keating, P.Kuchment T. Sunada and A. Teplyaev), Proceedings of Symposia in Pure Mathematics 77 (0712.1740)

  • Aperiodic order via dynamical systems: Diffraction theory for sets of finite local complexity, to appear: Contemp. Math. (0712.1323)

  • Hamiltonians on discrete structures: Jumps of the integrated density of states and uniform convergence (with Ivan Veselic), to appear in: Math. Z. (0709.2836)

  • Sch'nol's Theorem For Strongly Local Forms (with Anne Boutet de Monvel, Peter Stollmann), to appear in: Israel Journal of Mathematics, (0708.1501)

  • Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies (with Michael Baake, Christoph Richard), Lett. Math. Phys. Volume 82, (2007), 61--77. (0706.1677)

  • Continuity properties of the integrated density of states on manifolds (with Norbert Peyerimhoff, Olaf Post, Ivan Veselic), Japanese Journal of Mathematics, 3 (2008), 121--161. (0705.1079)

  • Pure point spectrum for measure dyamical systems on locally compact Abelian groups (with Nicolae Strungaru) (0704.2498)

  • Uniform existence of the integrated density of states for random Schrödinger operators on metric graphs over $\mathbb{Z}^d$ (with Michael J. Gruber, Ivan Veselic), J. Funct. Anal. Volume 253, (2007), 515--533. (math.0612743)

  • Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks, to appear in: Commun. Math. Phys. (math-ph/0608026)

  • Uniform existence of the integrated density of states for models on $\ZZ^d$ (with Peter Mueller and Ivan Veselic), to appear in: Positivity, (math-ph/0607063)

  • Mini-workshop: $L\sp 2$-Spectral Invariants and the Integrated Density of States. Abstracts from the mini-workshop held February 19--25, 2006. Organized by Jozef Dodziuk, Daniel Lenz, Thomas Schick and Ivan Veseli\'c. Oberwolfach Reports. Vol. 3, no. 1. (2006), no. 1, 511--552.

  • Pure point diffraction and cut and project schemes for measures: The smooth case (with Christoph Richard), Mathematische Zeitschrift 256, (2007), 347--378. (math.DS/0603453)

  • On an order based construction of a groupoid from an inverse semigroup, Proc. Edinburgh Math. Soc. 51 (2008), 387--406. (math.OA/0604105)

  • Uniform Szego Cocycles Over Strictly Ergodic Subshifts (with David Damanik), Journal of approximation theory 144, (2007), 133-138. (math.SP/0512033)

  • Characterizations of model sets by dynamical systems (with Michael Baake, Robert V. Moody), Ergodic Theory & Dynamical Systems 27, (2007), 341-382. (math.DS/0511648)

  • Mini-Workshop: Dynamics of Cocycles and One-Dimensional Spectral Theory. Abstracts from the mini-workshop held November 13--19, 2005. Organized by David Damanik, Russell Johnson and Daniel Lenz. Oberwolfach Reports. Vol. 2, no. 4. (2005), 2933--2978.

  • Generic subsets in spaces of measures and singular continuous spectrum (with Peter Stollmann), in: Lecture Notes in Physics 690, Springer (2006) (pdf-file)

  • Lower Transport Bounds for One-Dimensional Continuum Schr\"odinger Operators (with David Damanik, Guenter Stolz ), Math. Ann. 336, (2006), 361--389 (math-ph/0410062 )

  • Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature (with Steffen Klassert, Norbert Peyerimhoff, Peter Stollmann), Proceedings of the American Mathematical Society, 134, (2006) 1549--1559. (math-ph/0410022)

  • Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians (with Peter Stollmann), Duke Math. J. 131, (2006), 203--217. (math-ph/0410021)

  • Zero-measure Cantor spectrum for Schrodinger operators with low-complexity potentials (with David Damanik) J. Math. Pures Appl. (9) 85 (2006), 671--686 pdf-file

  • Deformation of Delone dynamical systems and pure point spectrum (with Michael Baake), Journal of Fourier Analysis and Applications, 11, (2005), 125 --150 (math.DS/0404155)

  • A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem (with David Damanik), Duke Math. J. 133 (2006), 95--123 pdf-file

  • An ergodic theorem for Delone dynamical systems and existence of the integrated density of states (with Peter Stollmann), J. d' Analyse Mathematique 97, (2006), 1 --23. (math-ph/0310017)

  • Singular continuous spectrum for certain quasicrystal Schrödinger operators, Contemporary Mathematics 364, 169--180, pdf-file

  • Substitution dynamical systems: Characterization of linear repetitivity and applications (with David Damanik), J. Math. Anal. Appl. 321 (2006), 766--780 (math.DS/0302231)

  • Aperiodic order and quasicrystals: spectral properties, Annales Henri Poincare 4, suppl 2 (2004). (with Peter Stollmann) ps-file , pdf-file

  • Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra (with Michael Baake), Ergodic Theory & Dynamical Systems 24 (2004), 1867-1893. (math.DS/0302061)

  • Ergodic theory and discrete one-dimensional random Schr"odinger operators: uniform existence of the Lyapunov exponent, Contemporary Mathematics 327 (2003), 223--238. ps-file pdf-file

  • Integrated density of states for random metrics on manifolds (with Norbert Peyerimhoff and Ivan Veselic), Proc. London Math. Soc. 88 (2004), 733--752. (math-ph/0212058)

  • Random Schr"odinger operators on manifolds (with Norbert Peyerimhoff and Ivan Veselic), Markov Process. Related Fields 9 (2003), 717--728, proceedings of the conference "Aspects Mathematiques des Systemes Aleatoires et de la Mecanique Statistique", held in the honour of L. Pastur, May 2002, Marseille (math-ph/0212057)

  • Delone dynamical systems: ergodic features and applications (with Steffen Klassert and Peter Stollmann), in: Quasicrystals, Structure and Physical Properties, H.-R. Trebin (ed.), Wiley-VCH, Berlin (2003), 172--187. ps-file , pdf-file

  • Algebras of random operators associated to Delone dynamical systems (with Peter Stollmann), Mathematical Physics, Analysis and Geometry 6 (2003), 269--290. (math-ph/0210031)

  • Aperiodic linearly repetitive Delone sets are densely repetitive, Discrete Comput. Geom. 31 (2004), 323--326. (math.MG/0208132)

  • Discontinuities of the integrated density of states for random operators on Delone sets (with Steffen Klassert and Peter Stollmann), Commun. Math. Phys. 241 (2003), 235--243. (math-ph/0208027)

  • Existence of non-uniform cocycles on uniquely ergodic systems, Ann. Inst. Henri Poincare: Prob. & Stat. 40 (2004), 197--206. ps-file

  • Powers in Sturmian sequences (with David Damanik), European J. Combin. 24 (2003), 377--390. ps-file

  • Groupoids, von Neumann Algebras and the Integrated Density of States (with Norbert Peyerimhoff and Ivan Veselic), Math. Phys. Anal. Geom. 10 (2007), 1--41. (arXiv:math-ph/0203026)

  • Delone dynamical systems and associated random operators (with Peter Stollmann), Conference Proceedings, Constanta (Romania), July 2-7, 2001, J.-M. Combes, J. Cuntz, G.A. Elliott, G. Nenciu, H. Siedentop, S. Stratila (eds.), Theta Foundation, ISBN 973-85432-2-3. (arXiv:math-ph/0202042)

  • Quasicrystals, aperiodic order, and groupoid von Neumann algebras (with Peter Stollmann), C. R. Acad. Sci. Ser. I, 334 (2002), 1131--1136. ps-file

  • Uniform spectral properties of one-dimensional quasicrystals, IV. quasi-Sturmian potentials (with David Damanik), J. d' Analyse Mathematique 90 (2003), 115--139. (arXiv:math-ph/0105034)

  • Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals, Commun. Math. Phys., 227 (2002), 119--130. (arXiv:math-ph/0106012)

  • Uniform ergodic theorems on subshifts over a finite alphabet, Ergodic Theory & Dynamical Systems, 22 (2002), 245--255. (arXiv:math.DS/0005067)

  • The index of Sturmian sequences (with David Damanik), European Journal of Combinatorics, 23 (2002), 23--29. ps-file

  • Linear repetitivity I., Uniform subadditive ergodic theorems and applications (with David Damanik), Discrete and Computational Geometry, 26 (2001), 411-428. (arXiv:math.DS/0005062)

  • Half-line eigenfunction estimates and singular continuous spectrum of zero Lebesgue mesasure (with David Damanik), Forum Mathematicum 16 (2004), 109--128 (arXiv:math.SP/9905099)

  • Uniform spectral properties of one-dimensional quasicrystals, III. $\alpha$-continuity (with David Damanik and Rowan Killip), Commun. Math. Phys. 212 (2000), 191-204. (arXiv:math-ph/9910017)

  • Uniform spectral properties of one-dimensional quasicrystals, II. The Lyapunov exponent (with David Damanik), Lett. Math, Phys. 50 (1999), 245-257. (arXiv:math-ph/9905008)

  • Uniform spectral properties of one-dimensional quasicrystals, I. Absence of eigenvalues (with David Damanik), Commun. Math. Phys. 207 (1999), 687-696. (arXiv:math-ph/9903011)

  • Hierarchical structures in Sturmian dynamical Systems, preprint 1999, revised version 2001, Theoret. Comput. Sci. 303 (2003). ps-file

  • Random Operators and Crossed Products, Mathematical Physics, Analysis and Geometry, 2 (1999), 197-220. (arXiv:math-ph/9902030)