Domaine : Équations aux dérivées partielles et Théorie spectrale

HDR : Quelques problèmes sur des temps semi-classiquement longs (pdf).

Exposés :  - Propagation estimates for the Schrödinger equation (pdf), Canberra, juillet 2009
                   - Strichartz estimates and the Isozaki-Kitada parametrix on asymptotically hyperbolic manifolds (pdf), Tokyo, avril 2010
                   - Low frequency resolvent estimates on asymptotically flat manifolds (pdf), Roscoff, juin 2013
                   - Strichartz inequalities on non compact manifolds (pdf), Rennes, avril 2014
                   - Wave packets on Riemannian manifolds (pdf), Lille, novembre 2015
                   - On the scattering theory of asymptotically  flat manifolds and Strichartz inequalities (pdf), Cergy, Juin 2016

Articles

() A wave packet approach to semiclassical propagation on Riemannian manifolds
en préparation.

(27) Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities (pdf)
avec H.Mizutani
  Trans. Amer. Math. Soc. (accepté)

(26) Global in time Strichartz inequalities on asymptotically flat manifolds with temperate trapping (pdf)
avec H. Mizutani

(25) Strichartz inequalities on surfaces with cusps (
pdf)

 Int. Math. Res. Not. IMRN, no. 24, 13437-13492 (2015)

(24) Sharp low frequency estimates on asymptotically flat manifolds (pdf)

avec J. Royer
  Comm. Math. Phys. vol. 335, issue 2, 809-850 (2015)

(23) Refined Sobolev inequalities on manifolds with ends (pdf)
avec Y. Sire, Math. Res. Let., vol. 21, no. 4, 663-675 (2014)

(22) Local energy decay for the damped wave equation (pdf)
avec J. Royer,
J. Funct. Analysis, 266, no. 7, 4538-4615 (2014)

(21) On the normal coordinates on manifolds with ends  (pdf)
Osaka Journal of Math., vol. 51, no. 4, 993-1015 (2014)

(20) Absence of eigenvalue at the bottom of the continuous spectrum on asymptotically hyperbolic manifolds (pdf)
Ann. Global Anal. Geom. 44, no. 2, 115–136 (2013)

(19) Low frequency estimates and local energy decay for asymptotically euclidean Laplacians (pdf)
Comm. in PDE Volume 36, Number 7, 1239-1286 (48), (2011)

(18) Low frequency estimates for long range perturbations in divergence form
(pdf)
Canadian J. Math. 63, 961-991 (2011)

(17) Low energy behaviour of powers of the resolvent of long range perturbations of the Laplacian (pdf)
Proceedings of the Centre for Mathematics and its Applications, Australian National University, Vol. 44 (2010)

(16) Strichartz estimates on asymptotically hyperbolic manifolds (pdf)
Analysis & PDE 4-1, 1-84 (2011)

(15) Semi-classical calculus on non compact manifolds with ends and weighted Lp estimates (pdf)
Annales de l'Institut Fourier, Vol. 61 no. 3, p. 1181-1223 (2011)

(14) Littlewood-Paley decompositions on manifolds with ends (pdf)
Bulletin de la SMF 138, fascicule 1, 1-37 (2010)

(13) On global Strichartz estimates for non trapping metrics (pdf)
avec N. Tzvetkov,
J. Funct. Analysis, 254, 6, 1661-1682 (2008)

(12) Semiclassical resonances of Schrödinger operators as zeroes of regularized determinants (pdf),
avec  V. Bruneau,
Int. Math. Res. Not. vol 2008, rnn002, 55 pages (2008)

(11) Strichartz estimates for long range perturbations (pdf)
avec N. Tzvetkov,
Amer. J. Math. vol 129, 6,  1565-1609 (2007)

(10) Resolvent estimates for the Laplacian on asymptotically hyperbolic manifolds (pdf)
Ann. H. Poincaré, no. 7,  527-561 (2006)

(9) Linear response theory for magnetic Schrödinger operators in disordered media (pdf)
avec F. Germinet,  A. Klein et  J. Schenker,
J. Funct. Analysis, 226, 301-372 (2005)

(8) Long time propagation and control on scarring for perturbed quantized hyperbolic toral automorphisms (pdf),
avec  S. De Bièvre,
Ann. H. Poincaré, no. 6, 885-913 (2005)

(7) Sub-exponential decay of operator kernels for functions of generalized Schrödinger operators (ps),
avec F. Germinet et A. Klein
,
Proc. AMS, 132, no. 9, 2703-2712 (2004)

(6) Generalized scattering phases for asymptotically hyperbolic manifolds,
CRAS,  338, no. 9, 685-688 (2004)

(5) Spectral distributions for long range perturbations  (ps),
J. Funct. Analysis, 212, no. 2, 431-471 (2004)

(4) Asymptotic behavior of regularized scattering phases for long range perturbations,
Journées EDP,
(Forges-les-Eaux, 2002), Exp. No. II, 12 pp., Univ. Nantes, Nantes (2002)

(3) Traces formulae for relatively Hilbert-Schmidt perturbations (ps),
Asymp. Analysis 32, no. 3-4,
257-291 (2002)

(2) Generalized scattering phase for long range perturbations of elliptic operators,
CRAS, Sér. I Math. 333, no. 9, 845-850 (2001)

(1) Fonction spectrale pour des perturbations relativement Hilbert-Schmidt,
CRAS, Sér. I Math. 332, no. 10, 887-892
(2001)



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