List of publications


  1. (with L. Banyai, D.B. Tran Thoai, and H. Haug) Interband quantum kinetics with LO-phonon scattering in a laser pulse excited semiconductor, Phys. stat. sol. (b) 173 (1992), 149 - 157.
  2. Spektraltheorie gewöhnlicher Differentialoperatoren mit Hilfe der m-Funktion (German), Ph.D. thesis, Osnabrück, 1996.
  3. Geometric characterization of singular self-adjoint boundary conditions for Hamiltonian systems, Appl. Anal. 60 (1996), 49 - 61.
  4. Essential spectrum and L2-solutions of one-dimensional Schrödinger operators, Proc. Amer. Math. Soc. 124 (1996), 2097 - 2100.
  5. Relationships between the m-function and subordinate solutions of second order differential operators, J. Math. Anal. Appl. 206 (1997), 352 - 363.
  6. A probabilistic approach to one-dimensional Schrödinger operators with sparse potentials, Comm. Math. Phys. 185 (1997), 313 - 323.
  7. (with H. Behncke) Asymptotic integration of linear differential equations, J. Math. Anal. Appl. 210 (1997), 585 - 597.
  8. Some Schrödinger operators with power-decaying potentials and pure point spectrum, Comm. Math. Phys. 186 (1997), 481 - 493.
  9. (with M. Christ and A. Kiselev) The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials, Math. Research Letters 4 (1997), 719 - 723.
  10. Some Schrödinger operators with power-decaying potentials and pure point spectrum, II. The discrete case, Helv. Phys. Acta 71 (1998), 200 - 213.
  11. The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials, Comm. Math. Phys. 193 (1998), 151 - 170.
  12. Spectral analysis of higher order differential operators, I. General properties of the M-function, J. London Math. Soc. 58 (1998), 367 - 380.
  13. (with A. Kiselev and B. Simon) Effective perturbation methods for one-dimensional Schrödinger operators, J. Differential Eq. 151 (1999), 290 - 312.
  14. Embedded singular continuous spectrum for one-dimensional Schrödinger operators, Trans. Amer. Math. Soc. 351 (1999), 2479 - 2497.
  15. One-dimensional Schrödinger operators with decaying potentials, in Operator Theory: Advances and Applications, vol. 108: Mathematical Results in Quantum Mechanics (Birkhäuser 1999), pg. 343 - 349.
  16. Spectral analysis of higher order differential operators, II. Fourth order equations, J. London Math. Soc. 59 (1999), 188 - 206.
  17. Bounds on embedded singular spectrum for one-dimensional Schrödinger operators, Proc. Amer. Math. Soc. 128 (2000), 161 - 171.
  18. (with S. Hassi and H. de Snoo) Subordinate solutions and spectral measures of canonical systems, Int. Eq. Op. Theory 37 (2000), 48 - 63.
  19. Schrödinger operators with decaying potentials: some counterexamples, Duke Math. J. 105 (2000), 463 - 496.
  20. (with H. Behncke) Uniform asymptotic integration of a family of linear differential systems, Math. Nachr. 225 (2001), 5 - 17.
  21. (with H. Behncke and D. Hinton) The spectrum of differential operators of order 2n with almost constant coefficients, J. Differential Eq. 175 (2001), 130 - 162.
  22. (with T. Kriecherbauer) Finite gap potentials and WKB asymptotics for one-dimensional Schrödinger operators, Comm. Math. Phys. 223 (2001), 409 - 435.
  23. (with D. Krutikov) Schrödinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure, Comm. Math. Phys. 223 (2001), 509 - 532.
  24. (with R. Killip) Reducing subspaces, J. Funct. Anal. 187 (2001), 396 - 405.
  25. Schrödinger operators and de Branges spaces, J. Funct. Anal. 196 (2002), 323 - 394.
  26. Inverse spectral theory for one-dimensional Schrödinger operators: the A function, Math. Z. 245 (2003), 597 - 617.
  27. Universal bounds on spectral measures of one-dimensional Schrödinger operators, J. Reine Angew. Math. 564 (2003), 105 - 117.
  28. (with A. Ben Amor) Direct and inverse spectral theory of one-dimensional Schrödinger operators with measures, Int. Eq. Op. Theory 52 (2005), 395 - 417.
  29. (with D. Damanik) Schrödinger operators with many bound states, Duke Math. J. 136 (2007), 51 - 80.
  30. Discrete and embedded eigenvalues for one-dimensional Schrödinger operators, Comm. Math. Phys. 271 (2007), 275 - 287.
  31. Finite propagation speed and kernel estimates for Schrödinger operators, Proc. Amer. Math. Soc. 135 (2007), 3329 - 3340.
  32. The absolutely continuous spectrum of one-dimensional Schrödinger operators, Math. Phys. Anal. Geom. 10 (2007), 359 - 373.
  33. (with A. Fischer) The absolutely continuous spectrum of discrete canonical systems, Trans. Amer. Math. Soc. 361 (2009), 793 - 818.
  34. (with A. Poltoratski) Reflectionless Herglotz functions and Jacobi matrices, Comm. Math. Phys. 288 (2009), 1007 - 1021.
  35. Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov Theorem, Proc. Amer. Math. Soc. 139 (2011), 2175 - 2182.
  36. The absolutely continuous spectrum of Jacobi matrices, Annals of Math. 174 (2011), 125 - 171.
  37. (with A. Poltoratski) Approximation results for reflectionless Jacobi matrices, Int. Math. Res. Not. 16 (2011), 3575 - 3617.
  38. (with I. Hur) Ergodic Jacobi matrices and conformal maps, Math. Phys. Anal. Geom. 15 (2012), 121 - 162.
  39. Topological properties of reflectionless Jacobi matrices, J. Approx. Theory 168 (2013), 1 - 17.
  40. Schrödinger operators and canonical systems, in Operator Theory (ed. Daniel Alpay), Springer 2015, pg. 623 - 630.
  41. (with I. Hur and M. McBride) The Marchenko representation of reflectionless Jacobi and Schrödinger operators, Trans. Amer. Math. Soc. 368 (2016), 1251 - 1270.
  42. Generalized reflection coefficients, Comm. Math. Phys. 337 (2015), 1011 - 1026.
  43. (with S. Grudsky and A. Rybkin) The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles, J. Math. Phys. 56 (2015), 14 pp.
  44. Spectral theory of canonical systems, de Gruyter Studies in Mathematics 70, de Gruyter, 2018.
  45. (with D. Ong) Generalized Toda flows, Trans. Amer. Math. Soc. 371 (2019), 5069 - 5081.
  46. Toda maps, cocycles, and canonical systems, J. Spectral Theory 9 (2019), 1327 - 1365.
  47. (with K. Scarbrough) The essential spectrum of canonical systems, J. Approx. Theory 254 (2020).
  48. (with K. Scarbrough) Oscillation theory and semibounded canonical systems, J. Spectral Theory 10 (2020), 1333 - 1359.
  49. Reflectionless Dirac operators and matrix valued Krein functions, to appear in Pure Appl. Funct. Anal., special issue dedicated to Barry Simon on the occasion of his 80th birthday.
  50. (with M. Forester) Topological properties of reflectionless canonical systems, submitted.
  51. (with J. Zeng) Reflectionless Dirac operators and canonical systems, submitted.
  52. Reflectionless operators and automorphic Herglotz functions, submitted.

The more recent papers (starting with 21) can be downloaded. Please go to preprints.