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Preprints

1. Reflectionless operators and automorphic Herglotz functions. pdf


2. 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: pdf


3. (with J. Zeng) Reflectionless Dirac operators and canonical systems. pdf


4. (with M. Forester) Topological properties of reflectionless canonical systems. pdf


5. (with K. Scarbrough) The essential spectrum of canonical systems.
   J. Approx. Theory 254 (2020): pdf


6. (with K. Scarbrough) Oscillation theory and semibounded canonical systems.
   J. Spectral Theory 10 (2020), 1333 - 1359: pdf


7. (with D. Ong) Generalized Toda flows.
   Trans. Amer. Math. Soc. 371 (2019), 5069 - 5081: pdf


8. Toda maps, cocycles, and canonical systems.
   J. Spectral Theory 9 (2019), 1327 - 1365: pdf


9. (with H. Jafarkhani, E. Koyuncu, and X. Liu) Outage-optimized distributed quantization of multicast beamforming vectors.
   IEEE Trans. Wireless Comm. 16 (2017), 2069 - 2082.
   This is an engineering (communication theory) paper; my contributions are minuscule, but I was generously invited to be a coauthor anyway: pdf


10. (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): pdf


11. Generalized reflection coefficients.
    Comm. Math. Phys. 337 (2015), 1011 - 1026: pdf


12. (with I. Hur and M. McBride) The Marchenko representation of reflectionless Jacobi and Schrödinger operators.
    Trans. Amer. Math. Soc. 368 (2016), 1251 - 1270: pdf


13. Schrödinger operators and canonical systems.
    Operator Theory (ed. Daniel Alpay), Springer 2015, 623 - 630.
    This is a brief review style article, somewhat informal: pdf


14. Topological properties of reflectionless Jacobi matrices.
    J. Approx. Theory 168 (2013), 1 - 17: pdf


15. (with I. Hur) Ergodic Jacobi matrices and conformal maps.
    Math. Phys. Anal. Geom. 15 (2012), 121 - 162: pdf


16. Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov Theorem.
    Proc. Amer. Math. Soc. 139 (2011), 2175 - 2182: pdf


17. (with A. Poltoratski) Approximation results for reflectionless Jacobi matrices.
    Int. Math. Res. Not. 16 (2011), 3575-3617: pdf


18. (with A. Poltoratski) Reflectionless Herglotz functions and generalized Lyapunov exponents.
    A shorter version of this paper appeared in Comm. Math. Phys. 288 (2009), 1007 - 1021.
    Click here for the pdf file of the original version (which has additional material).


19. The absolutely continuous spectrum of one-dimensional Schrödinger operators.
    Math. Phys. Anal. Geom. 10 (2007), 359 - 373: pdf


20. The absolutely continuous spectrum of Jacobi matrices.
    Annals of Math. 174 (2011), 125 - 171: pdf


21. Discrete and embedded eigenvalues for one-dimensional Schrödinger operators.
    Commun. Math. Phys. 271 (2007), 275 - 287: pdf


22. Finite propagation speed and kernel estimates for Schrödinger operators.
    Proc. Amer. Math. Soc. 135 (2007), 3329 - 3340: pdf


23. (with D. Damanik) Schrödinger operators with many bound states.
    Duke Math. J. 136 (2007), 51-80: pdf


24. (with A. Fischer) The absolutely continuous spectrum of discrete canonical systems.
    Trans. Amer. Math. Soc. 361 (2009), 793-818: pdf


25. (with A. Ben Amor) Direct and inverse spectral theory of one-dimensional Schrödinger operators with measures.
    Int. Eq. Op. Theory 52 (2005), 395-417: pdf


26. Universal bounds on spectral measures of one-dimensional Schrödinger operators.
    J. Reine Angew. Math. 564 (2003), 105-117: pdf


27. Inverse spectral theory for one-dimensional Schrödinger operators: the A function.
    Math. Z. 245 (2003), 597-617: pdf


28. Schrödinger operators and de Branges spaces.
    J. Funct. Anal. 196 (2002), 323-394: pdf


29. (with R. Killip) Reducing subspaces.
    J. Funct. Anal. 187 (2001), 396-405: pdf


30. (with D. Krutikov) Schrödinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure.
    Commun. Math. Phys. 223 (2001), 509 - 532: pdf


31. (with T. Kriecherbauer) Finite gap potentials and WKB asymptotics for one-dimensional Schrödinger operators.
    Commun. Math. Phys. 223 (2001), 409 - 435: pdf


32. (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: pdf