Overview

Due to popular demand this classic presentation of a vast amount on linear partial differential equations by a consummate master of the subject is now available as a study edition. The main change in this new edition is the inclusion of exercises with answers and hints. That is meant to emphasize that this volume can perfectly serve as a general course in modern analysis on a graduate student level and not only as a beginning of a specialised course in partial differential equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of general interest. As in the revised printing of volume II, a number of minor flaws have also been corrected in this edition. Parallely this edition is still available as volume 256 of the Grundlehren der mathematischen Wissenschaften. ""...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

Full Product Details

Author:   Lars Hormander
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2nd ed.
Dimensions:   Width: 15.50cm , Height: 2.80cm , Length: 23.50cm
Weight:   0.680kg
ISBN:  

9783540523437

ISBN 10:   354052343
Pages:   440
Publication Date:   10 August 1990
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

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.

Reviews

.,. 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 certainly will be a classic for many years. Zentralblatt fA1/4r Mathematik ., . 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 certainly will be a classic for many years. Zentralblatt f??r Mathematik ... 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 certainly will be a classic for many years. Zentralblatt fr Mathematik

.,. 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<br> It certainly will be a classic for many years. Zentralblatt fA1/4r Mathematik

.,. 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 certainly will be a classic for many years. Zentralblatt fA1/4r Mathematik ., . 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 certainly will be a classic for many years. Zentralblatt f??r Mathematik ... 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 certainly will be a classic for many years. Zentralblatt fr Mathematik

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