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

Papers and preprints

• Supersymmetric structures for second order differential operators, (with Frédéric Hérau and Johannes Sjöstrand), preprint, 2012 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, to appear. pdf
   
  
• Resolvent estimates for elliptic quadratic differential operators, (with Johannes Sjöstrand and Joe Viola), Analysis and PDE, to appear. 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