《線性發展方程的單參數半群》全面講述了強連續線性運算元的單參半群理論。《線性發展方程的單參數半群》的最大特點是在常微分和偏分方程運算元、衰退方程和volterra方程和控制理論中廣泛套用。而且，書中也強調了一些哲學動機和歷史背景。《線性發展方程的單參數半群》適用於數學、控制專業的研究生和更高層次的科研人員。
基本介紹
- 書名：線性發展方程的單參數半群
- 作者：恩格爾 (Engel K.J.)
- 出版日期：2013年10月1日
- 語種：簡體中文
- ISBN：9787510061479
- 外文名：One-Parmeter Semigroups for Linear Evolution Equations
- 出版社：世界圖書出版公司北京公司
- 頁數：586頁
- 開本：24
- 品牌：世界圖書出版公司北京公司
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《線性發展方程的單參數半群》由世界圖書出版公司北京公司出版。
作者簡介
作者：（義大利）恩格爾（Engel K.J.）
圖書目錄
Preface
Prelude
Ⅰ.Linear Dynamical Systems
1.Cauchy's Functional Equation
2.Finite-Dimensional Systems： Matrix Semigroups
3.Uniformly Continuous Operator Semigroups
4.More Semigroups
a.Multiplication Semigroups on Co（Ω）
b.Multiplication Semigroups on Lp（Ω，μ）
c.Translation Semigroups
5.Strongly Continuous Semigroups
a.Basic Properties
b.Standard Constructions
Notes
Ⅱ.Semigroups， Generators， and Resolvents
1.Generators of Semigroups and Their Resolvents
2.Examples Revisited
a.Standard Constructions
b.Standard Examples
3.Hille-Yosida Generation Theorems
a.Generation of Groups and Semigroups
b.Dissipative Operators and Contraction Semigroups
c.More Examples
4.Special Classes of Semigroups
a.Analytic Semigroups
c.Eventually Norm-Continuous Semigroups
d.Eventually Compact Semigroups
5.Interpolation and Extrapolation Spaces for Semigroups Simon Brendle
a.Analytic Semigroups
b.Favard and Abstract Holder Spaces
c.Fractional Powers
6.Well-Posedness for Evolution Equations
Notes
Ⅲ.Perturbation and Approximation of Semigroups
1.Bounded Perturbations
2.Perturbations of Contractive and Analytic Semigroups
3.More Perturbation
a.The Perturbation Theorem of Desch-Schappacher
b.Comparison of Semigroups
c.The Perturbation Theorem of Miyadera-Voigt
d.Additive Versus Multiplicative Perturbations
4.Trotter-Kato Approximation Theorems
a.A Technical Tool：Pseudoresolvents
b.The Approximation Theorems
c.Examples
5.Approximation Formulas
b.lnversion Formulas
Notes
Ⅳ.Spectral Theory for Semigroups and Generator8
1.Spectral Theory for Closed Operators
2.Spectrum of Semigroups and Generators
a.Basic Theory
b.Spectrum of Induced Semigroups
c.Spectrum of Periodic Semigroups
3.SpectraIMapping Theorems
a.Examples and Counterexamples
b.Spectral Mapping Theorems for Semigroups
c.Weak Spectral Mapping Theorem for Bounded Groups
4.Spectral Theory and Perturbation
Notes
Ⅴ.Asymptotics of Semigroups
1.Stability and Hyperbolicity for Semigroups
a.Stability Concepts
b.Characterization of Uniform Exponential Stability
c.Hyperbolic Decompositions
2.Compact Semigroups
a.General Semigroups
b.Weakly Compact Semigroups
c.Strongly Compa-ctSemigroups
3.Eventually Compact and Quasi-compact Semigroups
4.Mean Ergodic Semigroups
Ⅵ.Semigroups Everywhere
1.Semigroups for Population Equations
a.Semigroup Method for the CeU Equation
b.Intermezzo on Positive Semigroups
c.Asymptotics for the Cell Equation
2.Semigroups for the Transport Equation
a.Solution Semigroup for the Reactor Problem
b.Spectral and Asymptotic Behavior
3.Semigroups for Second-Order Cauchy Problems
a.The State Space X = XB1× X
b.The State Space X = X × X
c.The State Spce X=XC1×X
Notes
4.Semigroups for Ordinary Differential Operators M.Campiti， G.Metafune， D.Pallaru， and S.Romanelli
a.Nondegenerate Operators on R and R+
b.Nondegenerate Operators on Bounded Intervals
c.Degenerate Operators
d.Analyticity of Degenerate Semigroups
5.Semigroups for Partial Differential Operators Abdelaziz Rhandi
a.Notation and PreliminaryR，esults
b.Elliptic Differential Operators with Constant Coefficients
c.Elliptic Differential Operators with Variable Coefficients
Notes
6.Semigroups for DelayDifferential Equations
a.Well-Posedness of Abstract Delay Differential Equations
b.Regularity and Asymptotics
c.Positivityfor Delay Differential Equations
7.Semigroups for Volterra Equations
a.Mild and Classical Solutions
b.Optimal R，egularity
c.Integro-Differential Equations
Notes
8.Semigroups for Control Theory
a.Controllability
b.Observability
c.Stabilizability and Detectability
d.Transfer Functions and Stability
Notes
9.Semigroups for Nonautonomous Cauchy Problems
Rotand Schnaubelt
a.Cauchy Problems and Evolution Families
b.Evolution Semigroups
c.Perturbation Theory
d.Hyperbolic Evolution Families in the Parabolic Case
Notes
Ⅶ.A Brief History of the Exponential Function
Tanja Hahn and Carla Perazzoli
1.A Bird's-Eye View
2.The Functional Equation
3.The Differential Equation
4.The Birt，h of Semigroup Theory
Appendix
A.A Reminder of Some Functional Analysis
B.A Reminder of Some Operator Theory
C.Vector-Valued Integration
b.The Fourier Transform
c.The Laplace Transform
Epilogue
Determinism： Scenes from the Interplay Between Metaphysics and Mathematics
Gregor Nickel
1.The Mathematical Structure
2.Are R.elativity， Quantum Mechanics， and Chaos Deterministic？
3.Determinism in Mathematical Science from Newton to Einstein
4.Developments in the Concept of Object from Leibniz to Kant
5.Back to Some Roots of Our Problem： Motion in History
6.Bibliography and Further Reading
List of Symbols and Abbreviations
Prelude
Ⅰ.Linear Dynamical Systems
1.Cauchy's Functional Equation
2.Finite-Dimensional Systems： Matrix Semigroups
3.Uniformly Continuous Operator Semigroups
4.More Semigroups
a.Multiplication Semigroups on Co（Ω）
b.Multiplication Semigroups on Lp（Ω，μ）
c.Translation Semigroups
5.Strongly Continuous Semigroups
a.Basic Properties
b.Standard Constructions
Notes
Ⅱ.Semigroups， Generators， and Resolvents
1.Generators of Semigroups and Their Resolvents
2.Examples Revisited
a.Standard Constructions
b.Standard Examples
3.Hille-Yosida Generation Theorems
a.Generation of Groups and Semigroups
b.Dissipative Operators and Contraction Semigroups
c.More Examples
4.Special Classes of Semigroups
a.Analytic Semigroups
c.Eventually Norm-Continuous Semigroups
d.Eventually Compact Semigroups
5.Interpolation and Extrapolation Spaces for Semigroups Simon Brendle
a.Analytic Semigroups
b.Favard and Abstract Holder Spaces
c.Fractional Powers
6.Well-Posedness for Evolution Equations
Notes
Ⅲ.Perturbation and Approximation of Semigroups
1.Bounded Perturbations
2.Perturbations of Contractive and Analytic Semigroups
3.More Perturbation
a.The Perturbation Theorem of Desch-Schappacher
b.Comparison of Semigroups
c.The Perturbation Theorem of Miyadera-Voigt
d.Additive Versus Multiplicative Perturbations
4.Trotter-Kato Approximation Theorems
a.A Technical Tool：Pseudoresolvents
b.The Approximation Theorems
c.Examples
5.Approximation Formulas
b.lnversion Formulas
Notes
Ⅳ.Spectral Theory for Semigroups and Generator8
1.Spectral Theory for Closed Operators
2.Spectrum of Semigroups and Generators
a.Basic Theory
b.Spectrum of Induced Semigroups
c.Spectrum of Periodic Semigroups
3.SpectraIMapping Theorems
a.Examples and Counterexamples
b.Spectral Mapping Theorems for Semigroups
c.Weak Spectral Mapping Theorem for Bounded Groups
4.Spectral Theory and Perturbation
Notes
Ⅴ.Asymptotics of Semigroups
1.Stability and Hyperbolicity for Semigroups
a.Stability Concepts
b.Characterization of Uniform Exponential Stability
c.Hyperbolic Decompositions
2.Compact Semigroups
a.General Semigroups
b.Weakly Compact Semigroups
c.Strongly Compa-ctSemigroups
3.Eventually Compact and Quasi-compact Semigroups
4.Mean Ergodic Semigroups
Ⅵ.Semigroups Everywhere
1.Semigroups for Population Equations
a.Semigroup Method for the CeU Equation
b.Intermezzo on Positive Semigroups
c.Asymptotics for the Cell Equation
2.Semigroups for the Transport Equation
a.Solution Semigroup for the Reactor Problem
b.Spectral and Asymptotic Behavior
3.Semigroups for Second-Order Cauchy Problems
a.The State Space X = XB1× X
b.The State Space X = X × X
c.The State Spce X=XC1×X
Notes
4.Semigroups for Ordinary Differential Operators M.Campiti， G.Metafune， D.Pallaru， and S.Romanelli
a.Nondegenerate Operators on R and R+
b.Nondegenerate Operators on Bounded Intervals
c.Degenerate Operators
d.Analyticity of Degenerate Semigroups
5.Semigroups for Partial Differential Operators Abdelaziz Rhandi
a.Notation and PreliminaryR，esults
b.Elliptic Differential Operators with Constant Coefficients
c.Elliptic Differential Operators with Variable Coefficients
Notes
6.Semigroups for DelayDifferential Equations
a.Well-Posedness of Abstract Delay Differential Equations
b.Regularity and Asymptotics
c.Positivityfor Delay Differential Equations
7.Semigroups for Volterra Equations
a.Mild and Classical Solutions
b.Optimal R，egularity
c.Integro-Differential Equations
Notes
8.Semigroups for Control Theory
a.Controllability
b.Observability
c.Stabilizability and Detectability
d.Transfer Functions and Stability
Notes
9.Semigroups for Nonautonomous Cauchy Problems
Rotand Schnaubelt
a.Cauchy Problems and Evolution Families
b.Evolution Semigroups
c.Perturbation Theory
d.Hyperbolic Evolution Families in the Parabolic Case
Notes
Ⅶ.A Brief History of the Exponential Function
Tanja Hahn and Carla Perazzoli
1.A Bird's-Eye View
2.The Functional Equation
3.The Differential Equation
4.The Birt，h of Semigroup Theory
Appendix
A.A Reminder of Some Functional Analysis
B.A Reminder of Some Operator Theory
C.Vector-Valued Integration
b.The Fourier Transform
c.The Laplace Transform
Epilogue
Determinism： Scenes from the Interplay Between Metaphysics and Mathematics
Gregor Nickel
1.The Mathematical Structure
2.Are R.elativity， Quantum Mechanics， and Chaos Deterministic？
3.Determinism in Mathematical Science from Newton to Einstein
4.Developments in the Concept of Object from Leibniz to Kant
5.Back to Some Roots of Our Problem： Motion in History
6.Bibliography and Further Reading
List of Symbols and Abbreviations
