线性发展方程的单参数半群 英文【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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Ⅰ．Linear Dynamical Systems1

1．Cauchy's Functional Equation2

2．Finite-Dimensional Systems：Matrix Semigroups6

3．Uniformly Continuous Operator Semigroups14

4．More Semigroups24

a．Multiplication Semigroups on Co(Ω)24

b．Multiplication Semigroups on Lp(Ω,μ)30

c．Translation Semigroups33

5．Strongly Continuous Semigroups36

a．Basic Properties37

b．Standard Constructions42

Notes46

Ⅱ．ISemigroups,Generators,and Resolvents47

1．Generators of Semigroups and Their Resolvents48

2．Examples Revisited59

a．Standard Constructions59

b．Standard Examples65

3．Hille-Yosida Generation Theorems70

a．Generation of Groups and Semigroups71

b．Dissipative Operators and Contraction Semigroups82

c．More Examples89

4．Special Classes of Semigroups96

a．Analytic Semigroups96

b．Differentiable Semigroups109

c．Eventually Norm-Continuous Semigroups112

d．Eventually Compact Semigroups117

e．Examples120

5．Interpolation and Extrapolation Spaces for Semigroups123

Simon Brendle124

a．Sobolev Towers124

b．Favard and Abstract H？lder Spaces129

c．Fractional Powers137

6．Well-Posedness for Evolution Equations145

Notes154

Ⅲ．Perturbation and Approximation of Semigroups157

1．Bounded Perturbations157

2．Perturbations of Contractive and Analytic Semigroups169

3．More Perturbations182

a．The Perturbation Theorem of Desch-Schappacher182

b．Comparison of Semigroups192

c．The Perturbation Theorem of Miyadera-Voigt195

d．Additive Versus Multiplicative Perturbations201

4．Trotter-Kato Approximation Theorems205

a．A Technical Tool：Pseudoresolvents206

b．The Approximation Theorems209

c．Examples214

5．Approximation Formulas219

a．Chernoff Product Formula219

b．Inversion Formulas231

Notes236

Ⅳ．Spectral Theory for Semigroups and Generators238

1．Spectral Theory for Closed Operators239

2．Spectrum of Semigroups and Generators250

a．Basic Theory250

b．Spectrum of Induced Semigroups259

c．Spectrum of Periodic Semigroups266

3．Spectral Mapping Theorems270

a．Examples and Counterexamples270

b．Spectral Mapping Theorems for Semigroups275

c．Weak Spectral Mapping Theorem for Bounded Groups283

4．Spectral Theory and Perturbation289

Notes293

Ⅴ．Asymptotics of Semigroups295

1．Stability and Hyperbolicity for Semigroups296

a．Stability Concepts296

b．Characterization of Uniform Exponential Stability299

c．Hyperbolic Decompositions305

2．Compact Semigroups308

a．General Semigroups308

b．Weakly Compact Semigroups312

c．Strongly Compact Semigroups317

3．Eventually Compact and Quasi-compact Semigroups329

4．Mean Ergodic Semigroups337

Notes345

Ⅵ．Semigroups Everywhere347

1．Semigroups for Population Equations348

a．Semigroup Method for the Cell Equation349

b．Intermezzo on Positive Semigroups353

c．Asymptotics for the Cell Equation358

Notes361

2．Semigroups for the Transport Equation361

a．Solution Semigroup for the Reactor Problem361

b．Spectral and Asymptotic Behavior364

Notes367

3．Semigroups for Second-Order Cauchy Problems367

a．The State Space x=XB 1×X369

b．The State Space x=X×X372

c．The State Space x=XC 1×X374

Notes382

4．Semigroups for Ordinary Differential Operators383

M.Campiti,G.Metafune,D.Pallara,and S.Romanelli384

a．Nondegenerate Operators on R and R+384

b．Nondegenerate Operators on Bounded Intervals388

c．Degenerate Operators390

d．Analyticity of Degenerate Semigroups400

Notes403

5．Semigroups for Partial Differential Operators404

Abdelaziz Rhandi405

a．Notation and Preliminary Results405

b．Elliptic Differential Operators with Constant Coefficients408

c．Elliptic Differential Operators with Variable Coefficients411

Notes419

6．Semigroups for Delay Differential Equations419

a．Well-Posedness of Abstract Delay Differential Equations420

b．Regularity and Asymptotics424

c．Positivity for Delay Differential Equations428

Notes435

7．Semigroups for Volterra Equations435

a．Mlid and Classical Solutions436

b．Optimal Regularity442

c．Integro-Differential Equations447

Notes452

8．Semigroups for Control Theory452

a．Controllability456

b．Observability466

c．Stabilizability and Detectability468

d．Transfer Functions and Stability473

Notes476

9．Semigroups for Nonautonomous Cauchy Problems477

Roland Schnaubelt477

a．Cauchy Problems and Evolution Families477

b．Evolution Semigroups481

c．Perturbation Theory487

d．Hyperbolic Evolution Families in the Parabolic Case492

Notes496

Ⅶ．A Brief History of the Exponential Function497

Tanja Hahn and Carla Perazzoli497

1．A Bird's-Eye View497

2．The Functional Equation500

3．The Differential Equation502

4．The Birth ofSemigroup Theory506

Appendix509

A．A Reminder of Some Functional Analysis509

B．A Reminder of Some Operator Theory515

C．Vector-Valued Integration522

a．The Bochner Integral522

b．The Fourier Transform526

c．The Laplace Transform530

Epilogue531

Determinism：Scenes from the Interplay Between Metaphysics and Mathematics531

Gregor Nickel533

1．The Mathematical Structure533

2．Are Relativity,Quantum Mechanics,and Chaos Deterministic?536

3．Determinism in Mathematical Science from Newton to Einstein538

4．Developments in the Concept of Object from Leibniz to Kant546

5．Back to Some Roots of Our Problem：Motion in History549

6．Bibliography and Further Reading553

References555

List of Symbols and Abbreviations577

Index580