Microlocal analysis for differential operators : an introduction / Alain Grigis, Johannes Sjöstrand.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

1. Symbols and oscillatory integrals -- 2. The method of stationary phase -- 3. Pseudodifferential operators -- 4. Application to elliptic operators and L[superscript 2] continuity -- 5. Local symplectic geometry I (Hamilton-Jacobi theory) -- 6. The strictly hyperbolic Cauchy problem construction of a parametrix -- 7. The wavefront set (singular spectrum) of a distribution -- 8. Propagation of singularities for operators of real principle type -- 9. Local symplectic geometry II -- 10. Canonical transformations of pseudodifferential operators -- 11. Global theory of Fourier integral operators -- 12. Spectral theory for elliptic operators.

This short introduction to microlocal analysis is presented, in the spirit of Hörmander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjöstrand emphasise the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions. The contents of the book correspond to a graduate course given many times by the authors. It should prove to be useful to mathematicians and theoretical physicists, either to enrich their general knowledge of this area, or as preparation for the current research literature.