
M.
BURAK ERDOGAN
Associate Professor
Department
of Mathematics,
University of
Illinois,
1409 W. Green Street (MC-382)
Urbana, Illinois
61801
Office: 369 Altgeld
Hall
Phone: (217) 265-6761
E-mail: berdogan at math uiuc edu
Teaching:
Biographical
Information:
Research
Interests:
- Harmonic Analysis
- P. D. E's
Publications
(supported in part by NSF):
- (with W. Green)
"Dispersive estimates for the Schr\"odinger equation for
$C^{\frac{n-3}{2}}$ potentials in odd dimensions", preprint 2009,
submitted, [pdf]
- (with N. Tzirakis
and V. Zharnitsky)
"Near-linear dynamics in KdV with periodic boundary conditions",
preprint 2009, submitted, [pdf]
- (with J.
Chapman, D. Hart,
A. Iosevich
and D. Koh) "Pinned distance sets, k-simplices, Wolff's exponent in
finite fields and sum-product estimates", preprint 2009, submitted, [pdf]
- (with D. Hundertmark
and Y.-R.
Lee)
"Exponential decay of dispersion managed solitons for vanishing average
dispersion",
preprint 2008, submitted, [pdf]
- (with R. Oberlin)
"Estimates for the X-ray transform restricted to 2-manifolds", accepted
by Rev. Mat. Ibero., [pdf]
- (with M. Goldberg
and W. Schlag) "Strichartz
and smoothing estimates for Schrodinger operators with almost critical
magnetic potentials in three and higher dimensions", Forum Math., 21 (2009), no.
4, 687--722. [pdf]
- (with V. Zharnitsky)
"Quasi-linear dynamics in nonlinear Schr\" odinger equation with
periodic boundary conditions", Commun.
Math. Phys., 281 (2008),
no. 3, 655--673. [pdf]
- (with M. Goldberg and W. Schlag) "Strichartz and smoothing
estimates for Schrodinger operators with large magnetic potentials in R^3",
J. Eur. Math. Soc. (JEMS), 10
(2008), no. 2, 507--531., [pdf]
- (with M. Christ)
"Mixed norm estimates for certain generalized Radon transforms",
Trans. Amer. Math. Soc., 360
(2008), no. 10, 5477--5488. [pdf]
- (with W. Schlag) "Dispersive estimates for Schrodinger
operators in the presence of a resonance and/or an eigenvalue at zero
energy in dimension three: II", J. Anal. Math., 99 ,
199-248 (2006). [pdf]
- "A bilinear Fourier extension theorem and applications to the
distance set problem", IMRN, 2005:23, 1411-1425 (2005). [pdf]
- "On Falconer's distance set conjecture", Rev. Mat. Ibero.,
22, 649-662 (2006). [pdf]
- (with W. Schlag) "Dispersive estimates for Schrodinger
operators in the presence of a resonance and/or an eigenvalue at zero
energy in dimension three: I", Dynamics of PDE, 1, No. 4,
359-379 (2004). [pdf]
- "A note on the Fourier transform of fractal measures",
Math. Res. Lett., 11 no. 2-3, 299-313 (2004). [pdf]
- (with R. Killip
and W. Schlag) "Energy growth in Schrodinger's equation with
Markovian forcing", Commun.
Math. Phys., 240, 1-29 (2003). [pdf]
- "Mapping properties of the elliptic maximal function",
Rev. Mat. Ibero., 19, 221-234 (2003). [pdf]
- (with M. Christ)"Mixed norm estimates for a restricted X-ray
transform", J. d'Analyse, 87, 187-198 (2002). [pdf]
- "Mixed norm estimates for a restricted X-ray transform in R^4
and R^5", IMRN, 2001, No.11, 575-600. [pdf]
- "Analytic and asymptotic properties of non-symmetric Linnik's
densities", J. Fourier Anal. Appl., 5, 523-544 (1999).
- (with I.V.
Ostrovskii) "On mixture representation of the Linnik density",
J. Austral. Math. Soc. Ser. A, 64, no. 3, 317-326 (1998).
- (with I.V. Ostrovskii) "Analytic and asymptotic properties of
generalized Linnik Probability densities", J. Math. Anal. Appl., 217,
555-579 (1998).
- (with I.V. Ostrovskii) "Non-symmetric Linnik Distributions",
C.R. Acad. Sci. Paris, 325, Serie I, 511-516 (1997).
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