CONTENTS vii
Part 3. ADVANCED THEORY AND APPLICATIONS
Chapter 8. More on the symbol calculus 171
§8.1. Beals’s Theorem 171
§8.2. Real exponentiation of operators 177
§8.3. Generalized Sobolev spaces 182
§8.4. Wavefront sets, essential support, and microlocality 187
§8.5. Notes 196
Chapter 9. Changing variables 197
§9.1. Invariance, half-densities 197
§9.2. Changing symbols 203
§9.3. Invariant symbol classes 206
§9.4. Notes 217
Chapter 10. Fourier integral operators 219
§10.1. Operator dynamics 220
§10.2. An integral representation formula 226
§10.3. Strichartz estimates 235
§10.4.
Lp
estimates for quasimodes 240
§10.5. Notes 244
Chapter 11. Quantum and classical dynamics 245
§11.1. Egorov’s Theorem 245
§11.2. Quantizing symplectic mappings 251
§11.3. Quantizing linear symplectic mappings 257
§11.4. Egorov’s Theorem for longer times 264
§11.5. Notes 271
Chapter 12. Normal forms 273
§12.1. Overview 273
§12.2. Normal forms: real symbols 275
§12.3. Propagation of singularities 279
§12.4. Normal forms: complex symbols 282
§12.5. Quasimodes, pseudospectra 286
§12.6. Notes 289
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