Christian Remling: Preprints
- (with K. Scarbrough) The essential spectrum of canonical systems.
J. Approx. Theory 254 (2020):
- (with K. Scarbrough) Oscillation theory and semibounded canonical systems.
J. Spectral Theory 10 (2020), 1333 - 1359:
- (with D. Ong) Generalized Toda flows.
Trans. Amer. Math. Soc. 371 (2019), 5069 - 5081:
- Toda maps, cocycles, and canonical systems.
J. Spectral Theory 9 (2019), 1327 - 1365:
- (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:
- (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):
- Generalized reflection coefficients.
Comm. Math. Phys. 337 (2015), 1011 - 1026:
- (with I. Hur and M. McBride) The Marchenko representation of reflectionless Jacobi
and Schrödinger operators.
Trans. Amer. Math. Soc. 368 (2016), 1251 - 1270:
- Schrödinger operators and canonical systems.
Operator Theory (ed. Daniel Alpay), Springer 2015, 623 - 630.
This is a brief review style article, somewhat informal:
- Topological properties of reflectionless Jacobi matrices.
J. Approx. Theory 168 (2013), 1 - 17:
- (with I. Hur) Ergodic Jacobi matrices and conformal maps.
Math. Phys. Anal. Geom. 15 (2012), 121 - 162:
- Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov Theorem.
Proc. Amer. Math. Soc. 139 (2011), 2175 - 2182:
- (with A. Poltoratski) Approximation results for reflectionless Jacobi matrices.
Int. Math. Res. Not. 16 (2011), 3575-3617:
- (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).
- The absolutely continuous spectrum
of one-dimensional Schrödinger operators.
Math. Phys. Anal. Geom. 10 (2007), 359 - 373:
- The absolutely continuous spectrum
of Jacobi matrices.
Annals of Math. 174 (2011), 125 - 171:
- Discrete and embedded eigenvalues for one-dimensional
Commun. Math. Phys. 271 (2007), 275 - 287:
- Finite propagation speed and kernel estimates for
Proc. Amer. Math. Soc. 135 (2007), 3329 - 3340:
- (with D. Damanik) Schrödinger operators with many bound states.
Duke Math. J. 136 (2007), 51-80:
- (with A. Fischer) The absolutely continuous spectrum
of discrete canonical systems.
Trans. Amer. Math. Soc. 361 (2009), 793-818:
- (with A. Ben Amor) Direct and inverse spectral theory of
one-dimensional Schrödinger operators with measures.
Int. Eq. Op. Theory 52 (2005), 395-417:
- Universal bounds on spectral measures of
one-dimensional Schrödinger operators.
J. Reine Angew. Math. 564 (2003), 105-117:
- Inverse spectral theory for one-dimensional
Schrödinger operators: the A function.
Math. Z. 245 (2003), 597-617:
- Schrödinger operators and de Branges spaces.
J. Funct. Anal. 196 (2002), 323-394:
- (with R. Killip) Reducing subspaces.
J. Funct. Anal. 187 (2001), 396-405:
- (with D. Krutikov) Schrödinger operators with sparse
potentials: asymptotics of the Fourier transform of the spectral measure.
Commun. Math. Phys. 223 (2001), 509 - 532:
- (with T. Kriecherbauer) Finite gap potentials and WKB asymptotics
for one-dimensional Schrödinger operators.
Commun. Math. Phys. 223 (2001), 409 - 435:
- (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: