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The analysis of linear partial differential operators. I, Distribution theory and Fourier analysis

著者: Lars Hörmander
出版商: Berlin ; Heidelberg ; New York : Springer, cop. 1990.
丛书: Springer study edition.
版本/格式:   Print book : 英语 : Second edition查看所有的版本和格式
数据库:WorldCat
提要:

Part of a 4-volume treatise, this book, the Volume I, presents an exposition of the theory of distributions.

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所有的著者/提供者: Lars Hörmander
ISBN: 038752343X 9780387523439 354052343X 9783540523437
OCLC号码: 490243564
注意: Paru en 1983 dans la coll. "Grundlehren der mathematischen Wissenschaften" Band 256.
描述: 1 vol. (XI-440 p.) ; 24 cm.
内容: I. 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.- II. Definition and Basic Properties of Distributions.- Summary.- 2.1. Basic Definitions.- 2.2. Localization.- 2.3. Distributions with Compact Support.- Notes.- III. 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.- IV. 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.- V. Distributions in Product Spaces.- Summary.- 5.1. Tensor Products.- 5.2. The Kernel Theorem.- Notes.- VI. 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.- VII. The Fourier Transformation.- Summary.- 7.1. The Fourier Transformation in ? and in ?'.- 7.2. Poisson's Summation Formula and Periodic Distributions.- 7.3. The Fourier-Laplace Transformation in ?'.- 7.4. More General Fourier-Laplace Transforms.- 7.5. The Malgrange Preparation 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.- VIII. 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 CL.- 8.5. Rules of Computation for WFL.- 8.6. WFL for Solutions of Partial Differential Equations.- 8.7. Microhyperbolicity.- Notes.- IX. Hyperfunctions.- Summary.- 9.1. Analytic Functionals.- 9.2. General Hyperfunctions.- 9.3. The Analytic Wave Front Set of a Hyperfunction.- 9.4. The Analytic Cauchy Problem.- 9.5. Hyperfunction Solutions of Partial Differential Equations.- 9.6. The Analytic Wave Front Set and the Support.- Notes.- Exercises.- Answers and Hints to All the Exercises.- Index of Notation.
丛书名: Springer study edition.
责任: Lars Hörmander.
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.,." it is the best now available in print. ... All the theorems are there (among them the Schwartz kernel theorem), and all they have ... proofs." Bulletin of the American Mathematical Society"It 再读一些...

 
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