Birkhoff normal forms for Fourier integral operators II

J. Sjöstrand; A. Iantchenko

doi:10.1353/ajm.2002.0022

Birkhoff normal forms for Fourier integral operators II

J. Sjöstrand, A. Iantchenko

Department of Physics

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

We consider the problem of constructing a microlocal logarithm and a normal form for an elliptic semi-classical Fourier integral operator near a fixed point of the corresponding canonical transformation. In [Ia] the canonical transformation was assumed to be of real hyperbolic type. In [IS] this assumption was relaxed considerably, to what we think are the natural conditions.

Original language	English
Pages (from-to)	817-850
Number of pages	34
Journal	American Journal of Mathematics
Volume	124
Issue number	4
DOIs	https://doi.org/10.1353/ajm.2002.0022
Publication status	Published - Nov 2001

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title = "Birkhoff normal forms for Fourier integral operators II",

abstract = "We consider the problem of constructing a microlocal logarithm and a normal form for an elliptic semi-classical Fourier integral operator near a fixed point of the corresponding canonical transformation. In [Ia] the canonical transformation was assumed to be of real hyperbolic type. In [IS] this assumption was relaxed considerably, to what we think are the natural conditions.",

author = "J. Sj{\"o}strand and A. Iantchenko",

note = "Iantchenko, A.; Sj{\"o}strand, J., (2001) 'Birkhoff normal forms for Fourier integral operators II', American Journal of Mathematics 124(4) pp.817-850 RAE2008",

year = "2001",

month = nov,

doi = "10.1353/ajm.2002.0022",

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AU - Sjöstrand, J.

AU - Iantchenko, A.

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N2 - We consider the problem of constructing a microlocal logarithm and a normal form for an elliptic semi-classical Fourier integral operator near a fixed point of the corresponding canonical transformation. In [Ia] the canonical transformation was assumed to be of real hyperbolic type. In [IS] this assumption was relaxed considerably, to what we think are the natural conditions.

AB - We consider the problem of constructing a microlocal logarithm and a normal form for an elliptic semi-classical Fourier integral operator near a fixed point of the corresponding canonical transformation. In [Ia] the canonical transformation was assumed to be of real hyperbolic type. In [IS] this assumption was relaxed considerably, to what we think are the natural conditions.

U2 - 10.1353/ajm.2002.0022

DO - 10.1353/ajm.2002.0022

M3 - Article

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VL - 124

SP - 817

EP - 850

JO - American Journal of Mathematics

JF - American Journal of Mathematics

IS - 4

ER -

Birkhoff normal forms for Fourier integral operators II

Abstract

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