Karel
PRAVDA-STAROV
Professeur des UniversitésDirecteur de l'UFR Mathématiques IRMAR - Campus de Beaulieu Université de Rennes 1
Director office : Building 23, room 35 Personal office : Building 22, room 211/1 |
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38)
Spectral inequalities for combinations of Hermite functions and null-controllability for evolution equations enjoying Gelfand-Shilov smoothing effects,
(with
Jérémy Martin),
J. Inst. Math. Jussieu 22 (2023), no. 6, 2533-2582,
pdf
37)
Spectral inequality for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations,
(with
Karine Beauchard and Philippe Jaming),
Studia Math. 260 (2021), no. 1, 1-43,
pdf
36)
Geometric conditions for the exact controllability of fractional free and harmonic Schrödinger equations,
(with
Jérémy Martin),
J. Evol. Equ. 21 (2021), no. 1, 1059-1087,
pdf
35)
Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports,
(with
Karine Beauchard and Michela Egidi),
C. R. Math. Acad. Sci. Paris,
358 (2020), n. 6, 651-700,
pdf
34)
Estimations de résolvante et localisation du spectre pour certaines classes d'opérateurs pseudo-différentiels semi-classiques non autoadjoints, d'après Dencker, Sjöstrand et Zworski,
Séminaire Bourbaki, 72ème année, 2019-2020, Novembre 2019, Exposé no. 1169,
pdf
33)
Generalized Mehler formula for time-dependent non-selfadjoint quadratic operators and propagation of singularities,
Math. Ann. 372 (2018), no. 3-4, 1335-1382,
pdf
32)
From semigroups to subelliptic estimates for quadratic operators,
(with
Michael Hitrik
and Joe Viola),
Trans. Amer. Math. Soc. 370 (2018), no. 10,
7391-7415,
pdf
31)
Null-controllability of hypoelliptic quadratic differential equations,
(with
Karine Beauchard),
J. Éc. polytech. Math. 5 (2018), 1-43,
pdf
30)
Propagation of Gabor singularities for Schrödinger equations with quadratic Hamiltonians,
(with
Luigi Rodino
and
Patrik Wahlberg),
Math. Nachr. 291 (2018), 128-159,
pdf
29)
Short-time asymptotics of the regularizing effect for semigroups generated by quadratic operators,
(with
Michael Hitrik
and Joe Viola),
Bull. Sci. Math.
141 (2017), no. 7, 615-675,
pdf
28)
Null-controllability of non-autonomous Ornstein-Uhlenbeck equations,
(with
Karine Beauchard),
J. Math. Anal. Appl.
456 (2017), no. 1, 496-524,
pdf
27)
Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation,
(with Nicolas Lerner,
Yoshinori Morimoto and
Chao-Jiang Xu),
J. Funct. Anal.,
269 (2015), no. 2, 459-535,
pdf
26)
Some remarks on degenerate hypoelliptic Ornstein-Uhlenbeck operators,
(with
Michela Ottobre
and
Grigorios Pavliotis),
J. Math. Anal. Appl.
429 (2015), no. 2, 676-712,
pdf
25)
Semiclassical hypoelliptic estimates with a loss of many derivatives,
(with Alberto Parmeggiani),
Rev. Mat. Iberoam.
30 (2014), no. 4, 1439-1478, pdf
24)
Gelfand-Shilov smoothing properties of the radially symmetric spatially homogeneous Boltzmann equation without angular cutoff,
(with Nicolas Lerner,
Yoshinori Morimoto and
Chao-Jiang Xu),
J. Differential Equations, 256 (2014), no. 2, 797-831,
pdf
23)
De l'analyse microlocale de quelques classes d'équations aux dérivées partielles,
Habilitation dissertation, Université de Cergy-Pontoise, France (2013),
pdf
22)
A remark on the ultra-analytic smoothing properties of the spatially homogeneous Landau equation,
(with
Yoshinori Morimoto and
Chao-Jiang Xu),
Kinet. Relat. Models, 6 (2013), no. 4, 715-727,
pdf
21)
Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators,
(with Nicolas Lerner,
Yoshinori Morimoto and
Chao-Jiang Xu),
Kinet. Relat. Models, 6 (2013), no. 3, 625-648,
pdf
20)
Spectral and phase space analysis of the linearized non-cutoff Kac collision operator,
(with Nicolas Lerner,
Yoshinori Morimoto and
Chao-Jiang Xu),
J. Math. Pures Appl. 100, (2013), no. 6, 832-867,
pdf
19)
Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double
characteristics,
(with
Michael Hitrik),
Ann. Inst. Fourier, 63 (2013), no. 3, 985-1032,
pdf
18)
Exponential return to equilibrium for hypoelliptic quadratic systems,
(with Michela Ottobre and
Grigorios Pavliotis), J. Funct. Anal. 262 (2012), no. 9, 4000-4039,
pdf
17) Subelliptic estimates for overdetermined systems of quadratic differential operators,
Osaka J. Math. 49 (2012), no. 3, 563-611, pdf
16) Hypoelliptic estimates for a linear model of the
Boltzmann equation without angular cutoff, (with
Nicolas Lerner and
Yoshinori Morimoto), Comm. Partial Differential Equations,
37 (2012), no. 2, 234-284, pdf
15)
Hermite basis diagonalization for the non-cutoff radially symmetric linearized Boltzmann operator,
(with Nicolas Lerner,
Yoshinori Morimoto and
Chao-Jiang Xu),
Séminaire Laurent Schwartz - EDP et applications (2011-2012), Exp. No. 23, 10 pages, École Polytechnique, Palaiseau
14) Anisotropic hypoelliptic estimates for Landau-type operators,
(with
Frédéric Hérau),
J. Math. Pures Appl. 95 (2011), 513-552, pdf
13)
Sharp hypoelliptic estimates for some kinetic equations, (with
Nicolas Lerner),
(2011) Proceedings of the International Conference the
26th Matsuyama Camp, Ryukoku University, Kyoto,
pdf
12) Subelliptic estimates for quadratic differential operators,
Amer. J. Math. 133 (2011), no. 1, 39-89,
pdf
11)
Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics,
(with
Michael Hitrik),
Comm. Partial Differential Equations, 35 (2010), no. 6, 988-1028,
pdf
10) Spectra and semigroup smoothing
for non-elliptic quadratic operators, (with
Michael Hitrik),
Math. Ann.
344 (2009), no. 4, 801-846,
pdf
9) On the pseudospectrum
of elliptic quadratic differential operators,
Duke Math. J. 145 (2008), no. 2, 249-279
8) Pseudo-spectrum for a
class of semi-classical operators,
Bull. Soc. Math. France, 136 (2008), no. 3, 329-372
7) Contraction semigroups
of elliptic quadratic differential operators,
Math. Z. 259 (2008), no. 2, 363-391
6) Explicit examples of
nonsolvable weakly hyperbolic operators with real coefficients, Bull. Braz. Math. Soc. 38 (2007), no. 3, 397-425
5) Sur le pseudo-spectre de
certaines classes d'opérateurs pseudo-différentiels non auto-adjoints,
Séminaire : Équations aux Dérivées
Partielles, 2006-2007, Exp. No. XV, 33 p.,
École Polytechnique, Palaiseau
4) Boundary
pseudospectral behaviour for semi-classical operators in one
dimension,
Int. Math. Res. Not. (2007) Vol. 2007, article ID rnm029, 31 pages
3) Étude du pseudo-spectre d'opérateurs non
auto-adjoints, PhD Thesis, Université de Rennes 1, France (2006)
2) A complete study of the
pseudo-spectrum for the rotated harmonic oscillator, J. London Math. Soc. 73 (2006), no. 2, 745-761
1) A general result about the
pseudo-spectrum of Schrödinger operators, Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 460 (2004), 471-477
Séminaire d'équations aux dérivées partielles Groupe de travail "applications des mathématiques" Centre Henri Lebesgue Séminaire: Problèmes Spectraux en Physique Mathématique, Institut Henri Poincaré Vidéo-séminaire EDP Berkeley / Bonn / Zurich / Paris-Nord, Université de Paris-Nord
I am Professor in the Research Group in Partial Differential Equations and Dean of the Faculty of Mathematics of the University of Rennes 1.
The subject of my research deals with microlocal analysis. Here is my
cv
Editorial activities
I am a member of the Editorial Board of the Journal of Pseudo-Differential Operators and Applications
Publications
Analysis in Rennes
Analysis in Paris & London