Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T15:59:55.028Z Has data issue: false hasContentIssue false
  • English
  • Français

Semi-Classical Wavefront Set and Fourier Integral Operators

Published online by Cambridge University Press:  20 November 2018

Ivana Alexandrova
Ivana Alexandrova*
Affiliation:
Department of Mathematics, East Carolina University, Greenville, NC 27858, USA e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Here we define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators and prove a generalization of Egorov’s theorem to manifolds of different dimensions.

Keywords

35S3035A2758J4081Q20semi-classical distributionswavefront setFourier integral operatorsgeneralized Egorov theorem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 2 , 01 April 2008 , pp. 241 - 263
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Alexandrova, I., Structure of the semi-classical amplitude for general scattering relations. Comm. Partial Differential Equations 30(2005), no. 10-12, 1505–1535.Google Scholar
[2] Alexandrova, I., Structure of the short range amplitude for general scattering relations. Asymptot. Anal. 50(2006), no. 1-2, 13–30.Google Scholar
[3] Dozias, S., Opérateurs h-pseudodifférentiel à flot périodique . Ph.D. Thesis, Université de Paris Nord, 1994.Google Scholar
[4] Duistermaat, J., Fourier Integral Operators. Progress in Mathematics 130, Birkhäuser Boston, Boston, MA, 1996.Google Scholar
[5] Gerard, C., Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes. Mém. Soc. Math. France (N.S.) (1988), no. 31.Google Scholar
[6] Grigis, A. and Sjöstrand, J., Microlocal Analysis for Differential Operators. London Mathematical Society Lecture Note Series 196, Cambridge University Press, Cambridge, 1994.Google Scholar
[7] Hörmander, L., The Analysis of Linear Partial Differential Operators. Springer-Verlag, Berlin, 1985.Google Scholar
[8] Martinez, A., An Introduction to Semiclassical and Microlocal Analysis. Springer-Verlag, New York, 2002.Google Scholar
[9] Robert, D., Autour de l’Approximation Semi-Classique. Progress in Mathematics 68, Birkhäuser Boston, Boston, 1987.Google Scholar
[10] Sjöstrand, J. and Zworski, M., Quantum monodromy and semi-classical trace formulae. J. Math. Pures Appl. 81(2002), no. 1, 1–33.Google Scholar