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Michael Hitrik
Department of Mathematics
UCLA Los Angeles
CA 90095--1555, USA
Office : 6901 Phone
: + 1 310 206 0739 Email: hitrik" at "math.ucla.edu
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In the spring of 2013 I am teaching
Math 132 (Complex Analysis for Applications)
Homework Assignments for Math 132
I am organizing, together with Steve Zelditch, a workshop on
Analytic Microlocal Analysis at Northwestern University on May 20-24, 2013.
Research interests
Microlocal analysis and spectral theory
Papers and preprints
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Supersymmetric structures for second order differential operators,
(with Frédéric Hérau and Johannes Sjöstrand), preprint, 2012
pdf
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Quadratic PT-symmetric operators with real spectrum and similarity to self-adjoint operators, (with
Emanuela Caliceti,
Sandro Graffi, and Johannes Sjöstrand), J. Phys. A: Math. Theor., 45 (2012), 444007.
pdf
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Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics, (with
Karel Pravda-Starov),
Ann. Institut Fourier, to appear. pdf
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Resolvent estimates for elliptic quadratic differential operators,
(with Johannes Sjöstrand and Joe Viola), Analysis and PDE, to appear.
pdf
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Diophantine tori and Weyl asymptotics for non-selfadjoint operators in dimension two,
(with Johannes Sjöstrand), Comm. Math. Phys., 314 (2012), 373-417.
pdf
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Transmission eigenvalues for elliptic operators, (with Katya Krupchyk, Petri Ola, and Lassi Päivärinta), SIAM J. Math. Anal., 43 (2011), 2630-2639.
pdf
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Tunnel effect and symmetries for Kramers-Fokker-Planck type operators,
(with Frédéric Hérau and Johannes Sjöstrand), Journal Inst. Math. Jussieu, 1 (2011), 567-634.
pdf
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The interior transmission problem and bounds on transmission eigenvalues, (with
Katya Krupchyk, Petri Ola, and Lassi Päivärinta), Math. Res. Lett. 18 (2011), no. 2, 279-293.
pdf
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Transmission eigenvalues for operators with constant coefficients,
(with Katya Krupchyk, Petri Ola, and Lassi Päivärinta), SIAM J. Math. Anal. 42 (2010), no. 6, 2965-2986.
pdf
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Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics, (with
Karel Pravda-Starov),
Comm. Partial Differential Equations, 35 (2010), 988-1028.
pdf
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Spectra and Semigroup Smoothing for Non-elliptic Quadratic Operators, (with
Karel Pravda-Starov),
Math. Annalen, 344 (2009), 801-846.
pdf
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Tunnel Effect for Kramers-Fokker-Planck Operators: Return to Equilibrium and Applications,
(with Frédéric Hérau and Johannes Sjöstrand), Int. Math. Res. Not., 15 (2008), 48 pp.
pdf
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Rational Invariant Tori, Phase Space Tunneling, and Spectra for Non-Selfadjoint Operators in Dimension 2, (with
Johannes Sjöstrand),
Ann. Sc. Ecole Norm. Sup., 41(2008), 511-571.
pdf
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Tunnel Effect for Kramers--Fokker--Planck type Operators,
(with Frédéric Hérau and Johannes Sjöstrand), Ann. Henri Poincaré, 9 (2008), 209-274.
pdf
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Non-Selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions IIIa. One Branching Point, (with
Johannes Sjöstrand),
Can. J. Math., 60 (2008), 572-657.
pdf
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Diophantine Tori and Spectral Asymptotics for Non-Selfadjoint Operators,
(with Johannes Sjöstrand and San Vu Ngoc), Amer. J. Math., 129 (2007), 105-182.
pdf
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Energy Decay for Damped Wave Equations on Partially Rectangular Domains,
(with Nicolas Burq),
Math. Res. Letters, 14 (2007), 35-47. pdf
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Lagrangian Tori and Spectra for Non-Selfadjoint Operators (based on joint works with J. Sjöstrand and
S. Vu Ngoc), Séminaire Équations aux Dérivées Partielles, École Polytechnique, 14 pp., 2006.
pdf
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Non-Selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions II. Vanishing Averages, (with
Johannes Sjöstrand),
Comm. Partial Differential Equations, 30 (2005), 1065-1106.
pdf
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Boundary Spectral Behavior for Semiclassical Operators in Dimension One, Int. Math. Res. Not. 64 (2004), 3417-3438.
pdf
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Non-Selfadjoint Perturbations of Selfadjoint Operators in
2 Dimensions I, (with Johannes Sjöstrand), Ann. Henri Poincaré, 5 (2004), 1-73.
pdf
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Eigenfrequencies and Expansions for Damped Wave Equations, Meth. and Appl. of Analysis, 10 (2003), 543-564.
pdf
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Resolvent Expansions and Trace Regularizations for Schrödinger Operators,
(with Iosif Polterovich), Contemporary Mathematics, 327 (2003), 161-173.
pdf
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Regularized Traces and Taylor Expansions for the Heat
Semigroup, (with Iosif Polterovich), J. London Math. Soc. 68 (2003), 402-418. pdf
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Existence of Resonances in Magnetic Scattering, J.
Comp. Appl. Math. 148 (2002), 91-97. pdf
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Eigenfrequencies for Damped Wave Equations on Zoll
Manifolds, Asymptot. Analysis 31 (2002), 265-277.
pdf
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Expansions and Eigenfrequencies for Damped Wave Equations, Journées "Équations aux Dérivées
Partielles'' (Plestin-Les-Grèves, 2001), Exp. VI, 10 pp., 2001. pdf
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Properties of the Scattering Transform on the Real Line, J. Math. Anal. Appl. 258 (2001), 223-243.
pdf
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Stability of an Inverse Problem in Potential Scattering on
the Real Line, Comm. Partial Differential Equations
25 (2000), 925-955. pdf
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Bounds on Scattering Poles in One Dimension,
Comm. Math. Phys. 208 (1999), 381-411. pdf