- 作 者：L.Hormander著
- 出 版 社：世界图书出版公司北京公司
- 出版年份：2005
- ISBN：750627261X
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Introduction 1
Chapter XXV. Lagrangian Distributions and Fourier Integral Operators 3
Summary 3
25.1. Lagrangian Distributions 4
25.2. The Calculus of Fourier Integral Operators 17
25.3. Special Cases of the Calculus, and L2 Continuity 24
25.4. Distributions Associated with Positive Lagrangian Ideals 35
25.5. Fourier Integral Operators with Complex Phase 43
Notes 52
Chapter XXVI. Pseudo-Differential Operators of Principal Type 54
Summary 54
26.1. Operators with Real Principal Symbols 57
26.2. The Complex Involutive Case 73
26.3. The Symplectic Case 81
26.4. Solvability and Condition (ψ) 91
26.5. Geometrical Aspects of Condition (P) 110
26.6. The Singularities in N11 117
26.7. Degenerate Cauchy-Riemann Operators 123
26.8. The Nirenberg-Treves Estimate 134
26.9. The Singularities in Ne 2 and in Ne 12 137
26.10. The Singularities on One Dimensional Bicharacteristics 149
26.11. A Semi-Global Existence Theorem 161
Notes 163
Chapter XXVII. Subelliptic Operators 165
Summary 165
27.1. Definitions and Main Results 165
27.2. The Taylor Expansion of the Symbol 171
27.3. Subelliptic Operators Satisfying (P) 178
27.4. Local Properties of the Symbol 183
27.5. Local Subelliptic Estimates 202
27.6. Global Subelliptic Estimates 212
Notes 219
Chapter XXVIII. Uniqueness for the Cauchy problem 220
Summary 220
28.1. Calderón's Uniqueness Theorem 220
28.2. General Carleman Estimates 234
28.3. Uniqueness Under Convexity Conditions 239
28.4. Second Order Operators of Real Principal Type 242
Notes 248
Chapter XXIX. Spectral Asymptotics 249
Summary 249
29.1. The Spectral Measure and its Fourier Transform 249
29.2. The Case of a Periodic Hamilton Flow 263
29.3. The Weyl Formula for the Dirichlet Problem 271
Notes 274
Chapter XXX. Long Range Scattering Theory 276
Summary 276
30.1. Admissible Perturbations 277
30.2. The Boundary Value of the Resolvent, and the Point Spectrum 281
30.3. The Hamilton Flow 296
30.4. Modified Wave Operators 308
30.5. Distorted Fourier Transforms and Asymptotic Completeness 314
Notes 330
Bibliography 332
Index 350
Index of Notation 352