內容大鋼
赫爾曼德爾著的《線性偏微分運算元分析》介紹：This volume is an expanded version of Chapters Ⅲ, Ⅳ, Ⅴ and Ⅶ of my 1963 book "Linear partial differential operators". In addition there is an entirely new chapter on convolution equations, one on scattering theory, and one on methods from the theory of analytic functions of several complex variables. The latter is somewhat limited in scope though since it seems superfluous to duplicate the monographs by Ehrenpreis and by Palamodov on this subject.
作者介紹
(瑞典)赫爾曼德爾
赫爾曼德爾Born on January 24,1931, on the souther n coast of Sweden, Lars Hormander did his secondary schooling as well as his under- graduate and doctoral studies in Lund. His principle teacher and adviser at the University of Lund was Marcel Riesz until he returned, then Lars Garding. In 1956 he worked in the USA, at the universities of Chicago, Kansas, Minnesota and New York, before returning to a chair at the University of Stockhohn. He remained a frequent visitor to the US, particularly to Stanford and was Professor at the IAS, Princeton from 1964 to 1968. In 1968 he accepted a chair at the University of Lund, Sweden, where, today he is Emeritus Professor. Hormander's lifetime work has been devoted to the study of partial differential equations and its applications in complex analysis. In 1962 he was awarded the Fields Medal for his contributions to the general theory of linear partial differential operators. His book Linear Partial Differential Operators, published 1963 by Springer in the Grundlehren series, was the first major account of this theory. His four volume text The Analysis of Linear Partial Differential Operators, published in the same series 20 years later, illustrates the vast expansion of the subject in that period.
目錄
Introduction
Chapter Ⅹ. Existence and Approximation of Solutions of
Differential Equations
Summary
10.1. The Spaces Bp.k
10.2. Fundamental Solutions
10.3. The Equation P(D) u =f when f
10.4. Comparison of Differential Operators
10.5. Approximation of Solutions of Homogeneous
Differential Equations
10.6. The Equation P(D)u =f when f is in a Local Space
10.7. The Equation P(D)u=fwhenf(X)
10.8. The Geometrical Meaning of the Convexity Conditions
Notes
Chapter ?. Interior Regularity of Solutions of Differential
Equations
Summary
11.1. Hypoelliptic Operators
11.2. Partially Hypoelliptic Operators
11.3. Continuation of Differentiability
11.4. Estimates for Derivatives of High Order
Notes
Chapter ?. The Cauchy and Mixed Problems
Summary
12.1. The Cauchy Problem for the Wave Equation
12.2. The Oscillatory Cauchy Problem for the Wave Equation.
12.3. Necessary Conditions for Existence and Uniqueness
of Solutions to the Cauchy Problem
12.4. Properties of Hyperbolic Polynomials
12.5. The Cauchy Problem for a Hyperbolic Equation
12.6. The Singularities of the Fundamental Solution
12.7. A Global Uniqueness Theorem
12.8. The Characteristic Cauchy Problem
12.9. Mixed Problems
Notes
Chapter ?Ⅰ. Differential Operators of Constant Strength
Summary
13.1. Definitions and Basic Properties
13.2. Existence Theorems when the Coefficients are Merely
Continuous
13.3. Existence Theorems when the Coefficients are in C
13.4. Hypoellipticity
13.5. Global Existence Theorems
13.6. Non-uniqueness for the Cauchy Problem
Notes
Chapter ?Ⅴ. Scattering Theory
Summary
14.1. Some Function Spaces
14.2. Division by Functions with Simple Zeros
14.3. The Resolvent of the Unperturbed Operator
14.4. Short Range Perturbations
14.5. The Boundary Values of the Resolvent and the Point
Spectrum
14.6. The Distorted Fourier Transforms and the Continuous
Spectrum
14.7. Absence of Embedded Eigenvatues
Notes
Chapter XV. Analytic Function Theory and Differentia/
Equations
Summary
15.1. The Inhomogeneous Cauchy-Riemann Equations
15.2. The Fourier-Laplace Transform of B(X) when X is
Convex
15.3. Fourier-Laplace Representation of Solutions of
Differential Equations
15.4. The Fourier-Laplace Transform of C(X) when X is
Convex
Notes
Chapter ⅩⅥ. Convolution Equations
Summary
16.1. Subharmonic Functions
16.2. Plurisubharmonic Functions
16.3. The Support and Singular Support of a Convolution
16.4. The Approximation Theorem
16.5. The Inhomogeneous Convolution Equation
16.6. Hypoelliptic Convolution Equations
16.7. Hyperbolic Convolution Equations
Notes
Appendix A. Some Algebraic Lemmas
A.1. The Zeros of Analytic Functions
A.2. Asymptotic Properties of Algebraic Functions of
Several Variables
Notes
Bibliography
Index
Index of Notation
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