Michael Hitrik's home page

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

NSF Graduate Research Fellowship Workshop 2023

I am co-organizing a Workshop on Microlocal Analysis and Mathematical Physics, in honor of Anders Melin, to be held at Lund University, September 19-21, 2023.

Research interests

Microlocal analysis and spectral theory

Papers and preprints

Characterizing boundedness of metaplectic Toeplitz operators, (with Lewis Coburn and Johannes Sjöstrand), Int. Math. Res. Not., to appear. pdf
A direct approach to the analytic Bergman projection, (with Alix Deleporte and Johannes Sjöstrand), Ann. Fac. Sci. Toulouse Math., to appear. pdf
Complex FIOs and composition of Toeplitz operators, (with Lewis Coburn and Johannes Sjöstrand), J. Pseudo-Differ. Oper. Appl., 14 (2023), 31 pp. pdf
Semiclassical Gevrey operators in the complex domain, (with Richard Lascar, Johannes Sjöstrand, and Maher Zerzeri), Ann. Institut Fourier, 73 (2023), 1269-1318. pdf
Asymptotics for Bergman projections with smooth weights: a direct approach, (with Matthew Stone), Analysis and Mathematical Physics, 12 (2022), 33 pp. pdf
Adiabatic evolution and shape resonances, (with Andrea Mantile and Johannes Sjöstrand), Memoirs of the AMS, 280 (2022), no. 1380, 102 pp. pdf
Semiclassical Gevrey operators on exponentially weighted spaces of holomorphic functions, (with Richard Lascar, Johannes Sjöstrand, and Maher Zerzeri), Pure Appl. Funct. Analysis, 7 (2022), 641-653. pdf
Semiclassical Gevrey operators and magnetic translations, (with Richard Lascar, Johannes Sjöstrand, and Maher Zerzeri), Journal of Spectral Theory, 12 (2022), 53-82. pdf
Weyl symbols and boundedness of Toeplitz opeators, (with Lewis Coburn, Johannes Sjöstrand, and Francis White), Math. Res. Letters, 28 (2021), 681-696. pdf
Semigroup expansions for non-selfadjoint Schrödinger operators, (with Ben Bellis), J. Functional Analysis, 277 (2019), 3586-3598. pdf
Positivity, complex FIOs, and Toeplitz operators, (with Lewis Coburn and Johannes Sjöstrand), Pure and Applied Analysis, 1 (2019), 327-357. pdf
From semigroups to subelliptic estimates for quadratic operators, (with Karel Pravda-Starov and Joe Viola), Trans. AMS. 370 (2018), 7391-7415. pdf
Two minicourses on analytic microlocal analysis, (with Johannes Sjöstrand), "Algebraic and Analytic Microlocal Analysis", Springer Proceedings in Mathematics and Statistics, 269 (2018), 483-540. pdf
Rational invariant tori and band edge spectra for non-selfadjoint operators, (with Johannes Sjöstrand), J. Eur. Math. Soc. 20 (2018), 391-457.. pdf
Short-time asymptotics of the regularizing effect for semigroups generated by quadratic operators, (with Karel Pravda-Starov and Joe Viola), Bull. Sci. Math. 141 (2017), 615-675. pdf
Spectra for semiclassical operators with periodic bicharacteristics in dimension two, (with Michael Hall and Johannes Sjöstrand), Int. Math. Res. Not. 20 (2015), 10243-10277. pdf
Tunnel effect and symmetries for non-selfadjoint operators, Journées "Équations aux Dérivées Partielles'' (Biarritz, 2013), 10 pp., 2013. pdf
Supersymmetric structures for second order differential operators, (with Frédéric Hérau and Johannes Sjöstrand), Algebra i Analiz, 25 (2013), 125-154. pdf
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
Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics, (with Karel Pravda-Starov), Ann. Institut Fourier, 63 (2013), 985-1032. pdf
Resolvent estimates for elliptic quadratic differential operators, (with Johannes Sjöstrand and Joe Viola), Analysis and PDE, 6 (2013), 181-196. pdf
Diophantine tori and Weyl asymptotics for non-selfadjoint operators in dimension two, (with Johannes Sjöstrand), Comm. Math. Phys., 314 (2012), 373-417. pdf
Transmission eigenvalues for elliptic operators, (with Katya Krupchyk, Petri Ola, and Lassi Päivärinta), SIAM J. Math. Anal., 43 (2011), 2630-2639. pdf
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
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
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
Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics, (with Karel Pravda-Starov), Comm. Partial Differential Equations, 35 (2010), 988-1028. pdf
Spectra and Semigroup Smoothing for Non-elliptic Quadratic Operators, (with Karel Pravda-Starov), Math. Annalen, 344 (2009), 801-846. pdf
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
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
Tunnel Effect for Kramers--Fokker--Planck type Operators, (with Frédéric Hérau and Johannes Sjöstrand), Ann. Henri Poincaré, 9 (2008), 209-274. pdf
Non-Selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions IIIa. One Branching Point, (with Johannes Sjöstrand), Can. J. Math., 60 (2008), 572-657. pdf
Diophantine Tori and Spectral Asymptotics for Non-Selfadjoint Operators, (with Johannes Sjöstrand and San Vu Ngoc), Amer. J. Math., 129 (2007), 105-182. pdf
Energy Decay for Damped Wave Equations on Partially Rectangular Domains, (with Nicolas Burq), Math. Res. Letters, 14 (2007), 35-47. pdf
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
Non-Selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions II. Vanishing Averages, (with Johannes Sjöstrand), Comm. Partial Differential Equations, 30 (2005), 1065-1106. pdf
Boundary Spectral Behavior for Semiclassical Operators in Dimension One, Int. Math. Res. Not. 64 (2004), 3417-3438. pdf
Non-Selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions I, (with Johannes Sjöstrand), Ann. Henri Poincaré, 5 (2004), 1-73. pdf
Eigenfrequencies and Expansions for Damped Wave Equations, Meth. and Appl. of Analysis, 10 (2003), 543-564. pdf
Resolvent Expansions and Trace Regularizations for Schrödinger Operators, (with Iosif Polterovich), Contemporary Mathematics, 327 (2003), 161-173. pdf
Regularized Traces and Taylor Expansions for the Heat Semigroup, (with Iosif Polterovich), J. London Math. Soc. 68 (2003), 402-418. pdf
Existence of Resonances in Magnetic Scattering, J. Comp. Appl. Math. 148 (2002), 91-97. pdf
Eigenfrequencies for Damped Wave Equations on Zoll Manifolds, Asymptot. Analysis 31 (2002), 265-277. pdf
Expansions and Eigenfrequencies for Damped Wave Equations, Journées "Équations aux Dérivées Partielles'' (Plestin-Les-Grèves, 2001), Exp. VI, 10 pp., 2001. pdf
Properties of the Scattering Transform on the Real Line, J. Math. Anal. Appl. 258 (2001), 223-243. pdf
Stability of an Inverse Problem in Potential Scattering on the Real Line, Comm. Partial Differential Equations 25 (2000), 925-955. pdf
Bounds on Scattering Poles in One Dimension, Comm. Math. Phys. 208 (1999), 381-411. pdf