Preprints, Publications, and Manuscripts
Michael Christ
This material is based on work supported by the
National
Science Foundation under various grants. Any opinions, findings, and
conclusions
or recommendations expressed in this material are those of the
authors(s)
and do not necessarily reflect the views of the National Science
Foundation.
Expository articles:
Modulation invariant and multilinear
singular integral operators (after Lacey and Thiele), Seminaire
Bourbaki 962, June 2006
(first 2 pages are blank) pdf (figures are missing), postscript
(with A. Kiselev)
One-dimensional
Schrodinger operators with slowly decaying potentials: spectra and
asymptotics
(or: Baby Fourier analysis meets toy quantum
mechanics)
[Lecture notes for the 2002 University of Arkansas
Spring
lecture series. This is an expository account of work on
one-dimensional
Schrodinger operators.]
(postscript file)
(pdf file)
(with A. Kiselev)
One-dimensional
Schrodinger operators and nonlinear Fourier analysis (postscript file)
Counting to L^p, lecture notes for
the Instructional Conference on Combinatorial Aspects of Mathematical
Analysis, ICMS, Edinburgh, April 1-2, 2002. (postscript)
Preprints:
Bounds for multilinear sublevel sets
(revised October 2008)
Lebesgue space bounds for one-dimensional
generalized Radon transforms (September 2008)
Quasi-extremals for a Radon-like
transform
(September 2008)
Nonuniqueness of
generalized solutions of the Navier-Stokes equation (pdf)
(with J. Bennett, A. Carbery, and T. Tao), Finite
bounds for Holder-Brascamp-Lieb
multilinear inequalities (pdf)
A remark on sums of squares of
complex
vector fields (math.CV/0503506)
Nonuniqueness of weak solutions of the
nonlinear Schrodinger equation
On multilinear
oscillatory integrals (abstract of Oberwohlfach meeting lecture,
pdf)
Illposedness of a
Schrodinger equation with
derivative nonlinearity (postscript)
(with J. Colliander and T. Tao) Instability
of the periodic nonlinear
Schrodinger equation (postscript)
(with J. Colliander and T. Tao) Ill-posedness
for nonlinear Schrodinger and wave equations (postscript)
Analytic
Hypoellipticity in Dimension Two (pdf
file;
preprint)
Already in print:
Power series solution of a
nonlinear Schrodinger equation (math.AP/0503368)
(with J. Colliander and T. Tao) A priori
bounds and weak solutions
for the nonlinear Schrodinger equation in Sobolev spaces of negative
order
(with X. Li, T. Tao and C. Thiele) On
multilinear oscillatory integrals, singular and nonsingular
(Duke Math. J.; pdf)
(with A. Seeger) Necessary
conditions
for vector-valued operator inequalities in harmonic analysis (math.CA/0504030;
pdf)
Commentary on two papers of A.
P.
Calderon (June 2, 2005; pdf)
(with B. Erdogan) Mixed
norm estimates
for certain generalized Radon transforms
(with S. Fu) Compactness
in the d-bar Neumann problem,
magnetic Schrodinger operators, and the Aharonov-Bohm effect
(Advances in Math. 197 (2005), 1-40)
(with J. Colliander and T. Tao) Asymptotics,
frequency modulation, and low regularity ill-posedness for canonical
defocusing
equations
(Amer. J. Math. 125 (2003), 125
(2003), no. 6, 1235--1293; math.AP/0203044. postscript file)
(with A. Kiselev) Absolutely
continuous spectrum of Stark operators
(Ark. Mat. 41 (2003), 1-31; postscript file)
Slow off-diagonal decay for
Szego kernels associated to smooth Hermitian line bundles
(Contemporary Math. 320 (2003), 77-89; postscript)
(with A. Kiselev) Scattering
and wave operators for one-dimensional Schrodinger operators with
slowly
decaying nonsmooth potentials
(GAFA 12 (2002), 1174-1234)
(with B. Erdogan)
Mixed norm estimates for a restricted X-ray transform
(Journal d'Analyse 87 (2002), 187-198, postscript file)
Hypoellipticity
of the Kohn Laplacian for three-dimensional tubular CR structures
(Journal of the Institute of Mathematics of Jussieu 1
(2) (2002) 279-291; pdf file)
Spiraling
and nonhypoellipticity for CR structures degenerate along transverse
real
curves
(in Complex Analysis and Geometry, De Gruyter; pdf file)
Hypoellipticity
in the Infinitely Degenerate Regime
(in Complex Analysis and Geometry, De Gruyter; pdf file)
(with A. Kiselev) WKB
and spectral analysis of one-dimensional Schrodinger operators with
slowly
varying potentials
(Comm. Math. Phys. 218 (2001), 245-262; dvi file)
(with Michael Goldberg)
Vector
A_2 weights and a Hardy-Littlewood maximal function
(Trans. Amer. Math. Soc. 353 (2001), 1995-2002; dvi
file)
On
certain elementary trilinear operators
(Math. Research Letters 8 (2001), 43-56) (see also transparencies
)
(with A. Kiselev) Maximal
functions associated to filtrations
(J. Funct. Anal. 179 (2001); postscript file)
(with A. Kiselev) WKB
asymptotics of generalized eigenfunctions of one-dimensional
Schrodinger
operators
(J. Funct. Anal. 179 (2001); postscript file)
Hypoellipticity:
Geometrization and Speculation
(pdf file; Progress in Mathematics, vol. 188, pp.
91-109)
(with A. Kiselev and Y. Last)
Approximate
eigenvectors and spectral theory
(postscript file; in Differential Equations and
Mathematical
Physics,
edited by R. Weikard and G. Weinstein, Amer. Math.
Soc.,
Providence, RI, June 2000.)
Convolution,
Curvature, and Combinatorics. A Case Study
(postscript file; Internat. Math. Research Notices 19
(1998))
(with A. Carbery and J. Wright)Multidimensional
van der Corput and Sublevel Set Estimates
(pdf file) (Journal Amer. Math. Soc., 1999)
Global
Irregularity of the d-bar Neumann Problem For Worm Domains
(pdf
file)
A T(b) theorem with remarks on
analytic capacity (Colloq. Math. 50/51(1990), 601-628 ) (ps
file)
(There are some TeX glitches but the
manuscript is readable.)
Transparencies from lectures:
(with J. Colliander and T. Tao) An a priori inequalityand weak
solutions for the nonlinear Schrodinger equation (Berkeley-Paris
Nord-Bonn PDE seminar, November 15, 2006)
Radon-like transforms,
quasi-extremals, and (perhaps) subalgebraic sets (BIRS workshop,
September 2005)
Existence and nonuniqueness for a
nonlinear Schrodinger equation (MSRI workshop, August 2005)
Multilinear
oscillatory integrals (November 2003, postscript)
The d-bar Neumann problem, magnetic Schrodinger
operators,
and the Aharonov-Bohm effect (April 2003; postscript)
Convergence of Fourier
series: An ancient problem thrives in the modern world (postscript;
transparencies for 10/28/2002 UCB lecture)
(hand-drawn illustrations not included)
Three remarks on
degenerate
Kohn Laplacians (postscript file; lecture given at conference in
honor
of R. Gunning and J. J. Kohn)
Cauchy-Riemann
equations,
magnetic Schrodinger operators, and long-range correlations of random
zeros
(postscript file, revised January 2002)
On the simplest trilinear
operators (postscript file; transparencies for lecture June 27,
2001
at Mt. Holyoke SRC conference)
Convolution,
Curvature, and Counting (pdf file; transparencies for
lecture
at 1998 Kiel ICM satellite conference)
On the
eigenfunctions
and spectra of one-dimensional Schrodinger operators with slowly
decaying
potentials
(postscript file; transparencies for lecture November
6, 2000)