| Introduction ChapterⅠ Test Functions Summary 1.1 A review of Differential Calculus 1.2 Existence of Test Functions 1.3 Convolution 1.4 Cutoff Functions and Partitions of Unity Notes ChapterⅡ Definition and Basic Properties of Distributions Summary 2.1 Basic Definitions 2.2 Localization 2.3 Distributions with Compact Support Notes ChapterⅢ Differentiation and Multiplication by Functions Summary 3.1 Definition and Examples 3.2 Homogeneous Distributions 3.3 Some Fundamental Solutions 3.4 Evaluation of Some Integrals Notes ChapterⅣ Convolution Summary 4.1 Convolution with a Smooth Function 4.2 Convolution of Distributions 4.3 The Theorem of Supports 4.4 The Role of Fundamental Solutions 4.5 Basic Lp Estimates for Convolutions Notes ChapterⅤ Distributions in Product Spaces Summary 5.1 Tensor Products 5.2 The Kernel Theorem Notes ChapterⅥ Composition with Smooth Maps Summary 6.1 Definitions 6.2 Some Fundamental Solutions 6.3 Distributions on a Manifold 6.4 The Tangent and Cotangent Bundles Notes ChapterⅦ The Fourier Transformation Summary 7.1 The Fourier Transformation in and in 7.2 Poissons Summation Formula and Periodic Distributions 7.3 The Fourier-Laplace Transformation in 7.4 More General Fourier-Laplace Transforms 7.5 The Malgrange Preparatio Theorem 7.6 Fourier Transforms of Gaussian Functions 7.7 The Method of Stationary Phase 7.8 Oscillatory Integrals 7.9 H(s)Lp and Holder Estimates Notes ChapterⅧ Spectral Analysis of Singularities Summary 8.1 The Wave Front Set 8.2 A Review of Operations with Distributions 8.3 The Wave Front Set of Solutions Of Partial Differential Equations 8.4 THe Wave Front Set With Respect to 8.5 Rules of Computation for WFL 8.6 WFL for Solutions of Partial Differential Equations 8.7 Microhyperbolicity Notes ChapterⅨ Hyperfunctions Summary …… Exercises Answers and Hints to All the Exercises Bibliography Index Index of Notation |
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