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 book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.
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.
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.
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