Recent Research Papers (for earlier ones see MathSciNet) - Wilhelm Schlag

1. Semiclassical analysis of low and zero energy scattering for one dimensional Schroedinger operators with inverse square potentials (with Ovidiu Costin, Wolfgang Staubach, and Saleh Tanveer)
   preprint 2008.
2. Decay for the wave and Schroedinger evolutions on manifolds with conical ends, Part II (with Avy Soffer and Wolfgang Staubach)
   preprint 2008.
3. Decay for the wave and Schroedinger evolutions on manifolds with conical ends, Part I (with Avy Soffer and Wolfgang Staubach)
   preprint 2006, to appear in Trans. AMS
4. Two Erdoes problems on lacunary sequences: chromatic number and Diophantine approximation (with Yuval Peres)
   preprint 2007, to appear in Proc. London Math. Society
5. Strichartz and smoothing estimates for Schroedinger operators with almost
   critical magnetic potentials in three and higher dimensions (with Burak Erdogan and Michael Goldberg)
   preprint 2007, to appear in Forum Math.
6. Slow blow up solutions for the H^1(R^3) critical focusing semi-linear wave equation (with Joachim Krieger and Daniel Tataru)
   preprint 2007, to appear in Duke Math. Journal.
7. Renormalization and blow up for charge one equivariant critical wave maps (with Joachim Krieger and Daniel Tataru)
   preprint 2006, to appear in Inventiones Math.
8. Strichartz and smoothing estimates for Schroedinger operators with large magnetic potentials in R^3 (with Burak Erdogan and Michael Goldberg)
   preprint 2006, to appear in Journal of the EMS
9. On the formation of gaps in the spectrum of Schroedinger operators with quasi-periodic potentials (with Michael Goldstein)
   preprint 2006. To appear in Barry Simon's Festschrift on the occasion of his sixtieth birthday.
10. On resonances and the formation of gaps in the spectrum of quasi-periodic Schroedinger equations (with Michael Goldstein)
    preprint 2005, extensively revised version from 2008.
11. On Schroedinger operators with dynamically defined potentials (with Michael Goldstein)
    preprint 2005, to appear in Moscow Mathematical Journal, volume dedicated to Sinai's 70th birthday.
12. Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues (with Michael Goldstein)
    to appear in GAFA.
13. Spectral theory and nonlinear PDE: a survey
    preprint 2005, has appeared in Discrete and Cont. Dynamical Systems
14. A remark on Littlewood-Paley theory for the distorted Fourier transform
    preprint 2005, has appeared in Proceedings AMS
15. Non-generic blow-up solutions for the critical focusing NLS in 1-d (with J. Krieger)
    to appear in Journal of the EMS
16. On the focusing critical semi-linear wave equation (with J. Krieger)
    preprint 2005, to appear in American Journal of Math.
17. Numerical verification of a gap condition for linearized NLS (with L. Demanet)
    has appeared in Nonlinearity 19 (2006), 829-852.
18. Dispersive estimates for Schrodinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II
    as ps file . (with M Burak Erdogan)
    preprint 2005, to appear in Journal d'Analyse Math
19. Stable manifolds for all supercritical monic NLS in one dimension
    as pdf file, and the same paper in .ps format PS . (with Joachim Krieger)
    preprint 2005, has appeared in Journal of the AMS
20. Dispersive estimates for Schroedinger operators: a survey
    as pdf file, and the same paper in .ps format PS .
    preprint 2005, to appear in Proceedings of the PDE meeting at the IAS, Princeton, March 2004.
21. Dispersive estimates for Schrodinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: I
    as dvi file, and the same paper in PDF format PDF . (with Burak Erdogan)
    preprint 2004, has appeared in Dynamics of PDE
22. Agmon-Kato-Kuroda theorems for a large class of perturbations (with Alexander Ionescu)
    preprint 2004, has appeared in Duke Math. Journal, 2006.
23. Stable manifolds for an orbitally unstable NLS
    preprint 2004, to appear in Annals of Math.
24. Dispersive estimates for Schroedinger operators in two dimensions
    as dvi file, and the same paper in PDF format PDF .
    preprint 2004, has appeared in Comm. Math. Phys.
25. A Limiting Absorption Principle for the three-dimensional Schroedinger equation with L^p potentials (with Michael Goldberg)
    has appeared in Int. Math. Research Notices.
26. On discrete Schroedinger operators with stochastic potentials
    as ps file, and the same paper in PDF format PDF .
    has appeared in proceedings of ICMP Lisbon, 2003.
27. Dispersive estimates for Schroedinger operators in dimensions one and three
    as ps file, and the same paper in PDF format PDF . (with Michael Goldberg)
    has appeared in Comm. Math. Phys. vol. 251, no. 1 (2004), 157-178.
28. Asymptotic stability of N-soliton states of NLS
    as ps file, and the same paper in PDF format PDF . (with Igor Rodnianski and Avy Soffer)
    preprint 2003.
29. Dispersive analysis of charge transfer models
    as ps file, and the same paper in PDF format PDF . (with Igor Rodnianski and Avy Soffer)
    has appeared in Comm. Pure and Appl. Math.
30. Energy growth in Schroedinger's equation with Markovian forcing
    as ps file, and the same paper in PDF format PDF . (with Burak Erdogan and Rowan Killip)
    has appeared in Comm. Math. Phys. 240 (2003), no. 1-2, 1-29.
31. On the Hardy-Littlewood majorant problem for random sets
    as dvi file, and the same paper in PDF format PDF . (with Gerd Mockenhaupt)
    preprint, 2003, Journal of Functional Analysis.
32. On continuum incidence problems related to harmonic analysis
    the same paper in PDF format PDF .
    has appeared in J. Func. Analysis 201 (2003), no. 2, 480-521.
33. Time decay for solutions of Schroedinger equations with rough and time-dependent potentials
    the same paper in PDF format PDF .
    has appeared in Invent. Math. 155 (2004), no. 3, 451-513. (with Igor Rodnianski)
34. Classical and quantum scattering for a class of long range random potentials
    the same paper in PDF format PDF .
    has appeared in Int. Math. Res. Notices 2003, no. 5, 243-300. (with Igor Rodnianski)
35. On the integrated density of states for Schroedinger operators on Z^2 with quasi periodic potential.
    has appeared in Comm. Math. Phys. 223 (2001), no. 1, 47-65.
36. Frequency concentration and localization lengths for the Anderson model at small disorders.
    has appeared in Journal d'analyse math. 88 (2002), 173-220. (with C. Shubin and T. Wolff)
37. Anderson localization for Schroedinger operators on Z^2 with quasi-periodic potential.
    has appeared in Acta Mathematica 188 (2002), no. 1, 41-86. (with J. Bourgain and M. Goldstein)
38. Bernoulli convolutions and an intermediate value theorem for entropies of K-partitions.
    has appeared in Journal d'analyse math. 87 (2002), 337-367. (with E. Lindenstrauss and Y. Peres)
39. Anderson localization for Schroedinger operators on Z with potentials given by the skew-shift.
    has appeared in Comm. Math. Phys. 220 (2001), no. 3, 583-621. (with J. Bourgain and M. Goldstein)
40. Anderson localization for Schroedinger operators on Z with strongly mixing potentials.
    has appeared in Comm. Math. Phys. 215 (2000), 143-175. (with J. Bourgain)
41. Holder continuity of the integrated density of states for quasiperiodic Schroedinger equations and averages of shifts of subharmonic functions.
    has appeared in Annals of Math. (2) 154 (2001), no. 1, 155-203. (with M. Goldstein)