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Preprints

1. Polynomial Toda maps are transfer matrices.
   To appear in Proc. Amer. Math. Soc.: pdf


2. Reflectionless operators and automorphic Herglotz functions.
   Int. Math. Res. Not., (2025), no. 21, 20 pages: pdf


3. 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


4. (with J. Zeng) Reflectionless Dirac operators and canonical systems.
   J. Spectral Theory 15 (2025), 1305 -1336: pdf


5. (with M. Forester) Topological properties of reflectionless canonical systems.
   To appear in Trans. Amer. Math. Soc.: pdf


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


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


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


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


10. (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


11. (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


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


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


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


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


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


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


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


19. (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).


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


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


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


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


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


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


26. (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


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


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


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


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


31. (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


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


33. (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