正版新书]线性偏微分算子分析(第2卷)(英文版)(瑞典)赫尔曼德尔9

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 Ⅺ. 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 Ⅻ. 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 ⅫⅠ. 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 ⅪⅤ. 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

赫尔曼德尔BornonJanuary24,1931,onthesoutherncoastofSweden,LarsHormanderdidhissecondaryschoolingaswellashisunder-graduateanddoctoralstudiesinLund.HisprincipleteacherandadviserattheUniversityofLundwasMarcelRieszuntilhereturned,thenLarsGarding.In1956heworkedintheUSA,attheuniversitiesofChicago,Kansas,MinnesotaandNewYork,beforereturningtoachairattheUniversityofStockhohn.HeremainedafrequentvisitortotheUS,particularlytoStanfordandwasProfessorattheIAS,Princetonfrom1964to1968.In1968heacceptedachairattheUniversityofLund,Sweden,where,todayheisEmeritusProfessor.Hormander'slifetimeworkhasbeendevotedtothestudyofpartialdifferentialequationsanditsapplicationsincomplexanalysis.In1962hewasawardedtheFieldsMedalforhiscontributionstothegeneraltheoryoflinearpartialdifferentialoperators.HisbookLinearPartialDifferentialOperators,published1963bySpringerintheGrundlehrenseries,wasthefirstmajoraccountofthistheory.HisfourvolumetextTheAnalysisofLinearPartialDifferentialOperators,publishedinthesameseries20yearslater,illustratesthevastexpansionofthesubjectinthatperiod.