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These notes correspond roughly to the two minicourses prepared by the authors for the workshop on Analytic Microlocal Analysis, held at Northwestern University in May 2013.
S. Mandelbrojt, Analytic functions and classes of infinitely differentiable functions,
1942
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S. Mandelbrojt, Séries adhérentes. Régularisation des suites. Applications,
1952
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L. Ehrenpreis, Solutions of some problems of division IV. Invertible and elliptic operators,
1960
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L. Hörmander, Differential equations without solutions,
1960
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L. Hörmander, Differential operators of principal type,
1960
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J. Boman, On the intersection of classes of infinitely differentiable functions,
1964
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L. Boutet de Monvel, P. Krée, Pseudo-differential operators and Gevrey classes,
1967
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D. Iagolnitzer, H.P. Stapp, Macroscopic causality and physical region analyticity in S S -matrix theory,
1969
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K.G. Andersson, Propagation of analyticity of solutions of partial differential equations with constant coefficients,
1970
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L. Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations
1971
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L. Hörmander, Uniqueness theorems and wave front sets for soutions of linear partial differential equations with analytic coefficients,
1971
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L. Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations,
1971
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M. Sato, T. Kawai, M. Kashiwara, Microfunctions and pseudo-differential equations,
1973
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J. Bros, D. Iagolnitzer, Tuboïdes et structure analytique des distributions. II. Support essentiel et structure analytique des distributions,
1975
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D. Iagolnitzer, H.P. Stapp, The pole-factorization theorem in S S -matrix theory,
1977
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A. Cordoba and C. Fefferman, Wave packets and Fourier integral operators
1978
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R. Melrose, J. Sjöstrand, Singularities of boundary value problems I,
1978
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F. Trèves, Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the ∂ ¯ \overline{\partial} -Neumann problem,
1978
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J. Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems,
1980
Earlier work this paper cites.
J. Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems II,
1980
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J. Sjöstrand, Analytic singularities and microhyperbolic boundary value problems,
1980
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D.S. Tartakoff, The local real analyticity of solutions to □ b \square_{b} and the ∂ ¯ \bar{\partial} -Neumann problem,
1980
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F. Treves, Introduction to pseudodifferential and Fourier integral operators. Vol. 1. Pseudodifferential operators,
1980
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A. Grigis, P. Schapira, J. Sjöstrand, Propagation de singularités analytiques pour des opérateurs à caractéristiques multiples,
1981
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N. Hanges, Propagation of analyticity along real bicharacteristics,
1981
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G. Métivier, Analytic hypoellipticity for operators with multiple characteristics,
1981
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J. Rauch, J. Sjöstrand, Propagation of analytic singularities along diffracted rays
1981
Earlier work this paper cites.
J. Sjöstrand, Analytic singularities of solutions of boundary value problems,
1981
Earlier work this paper cites.
J. Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems III,
1981
Cited alongside, same era.
J. Sjöstrand, Singularités analytiques microlocales
1982
Cited alongside, same era.
N. Hanges, J. Sjöstrand, Propagation of analyticity for a class of non-micro-characteristic operators,
1982
Cited alongside, same era.
R. Melrose, J. Sjöstrand, Singularities of boundary value problems II,
1982
Cited alongside, same era.
J. Sjöstrand, Singularités analytiques microlocales,
1982
Cited alongside, same era.
J. Sjöstrand, Analytic wavefront sets and operators with multiple characteristics,
1983
Cited alongside, same era.
A. Melin and J. Sjöstrand, Determinats of pseudodifferential operators and complex deformations of phase space
2002
Later among the works it cites.
J. Sjöstrand, Lectures on resonances
2002
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A. Martinez, An introduction to semiclassical and microlocal analysis,
2002
Later among the works it cites.
A. Melin, J. Sjöstrand, Determinants of pseudodifferential operators and complex deformations of phase space,
2002
Later among the works it cites.
A. Lahmar-Benbernou, A. Martinez, On Helffer-Sjöstrand’s theory of resonances,
2002
Later among the works it cites.
A. Melin and J. Sjöstrand, Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension
2003
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G. Lebeau, Régularité Gevrey 3 3 pour la diffraction,
1984
Cited alongside, same era.
A. Grigis, J. Sjöstrand, Front d’onde analytique et sommes de carrés de champs de vecteurs,
1985
Cited alongside, same era.
B. Helffer, J. Sjöstrand, Résonances en limite semiclassique,
1986
Cited alongside, same era.
C. Gérard, J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type,
1987
Cited alongside, same era.
C. Gérard, J. Sjöstrand, Résonances en limite semiclassique et exposants de Lyapunov,
1988
Cited alongside, same era.
J. Sjöstrand, Estimates on the number of resonances for semiclassical Schrödinger operators,
1988
Cited alongside, same era.
Later among the works it cites.
A. Melin, J. Sjöstrand, Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2,
2003
Later among the works it cites.
N. Dencker, J. Sjöstrand, and M. Zworski, Pseudo-spectra of semiclassical (pseudo)differential operators
2004
Later among the works it cites.
M. Hitrik, Boundary spectral behavior for semiclassical operators in dimension one
2004
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M. Hitrik and J. Sjöstrand, Non-selfadjoint perturbations of selfadjoint operators in
2004
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N. Dencker, J. Sjöstrand, M. Zworski, Pseudospectra of semiclassical (pseudo-) differential operators,
2004
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M. Hitrik, J. Sjöstrand, Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions I,
2004
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M. Hitrik, Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions II. Vanishing averages,
2005
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M. Hitrik, J. Sjöstrand, and S. Vũ Ngọc, Diophantine tori and spectral asymptotics for non-selfadjoint operators
2007
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C. Kenig, J. Sjöstrand, and G. Uhlmann, The Calderón problem with partial data
2007
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M. Hitrik, J. Sjöstrand, S. Vũ Ngọc, Diophantine tori and spectral asymptotics for non-selfadjoint operators,
2007
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M. Hitrik, J. Sjöstrand, Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions IIIa. One branching point,
2008
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M. Hitrik, J. Sjöstrand, Rational invariant tori, phase space tunneling, and spectra for non-selfadjoint operators in dimension 2,
2008
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J. Sjöstrand, Pseudodifferential operators and weighted normed symbol spaces,
2008
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A. Martinez, S. Nakamura, V. Sordoni, Analytic wave front set for solutions to Schrödinger equations,
2009
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A. Martinez, S. Nakamura, V. Sordoni, Analytic wave front set for solutions to Schrödinger equations II—long range perturbations,
2010
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E. Caliceti, S. Graffi, M. Hitrik, J. Sjöstrand, Quadratic 𝒫𝒯 {\cal PT} –symmetric operators with real spectrum and similarity to self-adjoint operators
2012
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M. Zworski, Semiclassical analysis
2012
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M. Hitrik, J. Sjöstrand, Diophantine tori and Weyl laws for non-selfadjoint operators in dimension two,
2012
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M. Hitrik, E. Caliceti, S. Graffi, J. Sjöstrand Quadratic PT–symmetric operators with real spectrum and similarity to self-adjoint operators,
2012
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J.-F. Bony, S. Fujiié, T. Ramond, M. Zerzeri, Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances,
2012
Later among the works it cites.
J. Sjöstrand, G. Uhlmann, Local analytic regularity in the linearized Calderón problem,
2013
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M. Hitrik and J. Sjöstrand, Rational invariant tori and band edge spectra for non-selfadjoint operators
2015
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