Microlocal Analysis for Differential Operators An Introduction [Paperback]

This book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.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.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.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 emphasize the basic tools, especially the method of stationary phase, and they discuss wavefront sets, elliptic operators, local symplectic geometry, and WKB-constructions.Introduction; 1. Symbols and oscillatory integrals; 2. The method of stationary phase; 3. Pseudodifferential operators; 4. Application to elliptic operators and L2 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; Bibliography. ...an excellent introduction to microlocal analysis for graduate students and for mathematicians who wish to understand the basic ideas of calculus with classical l3+