线性偏微分算子分析 第4卷pdf电子书版本下载

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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