Applied Functional Analysis
Springer-Verlag New York Inc.
978-1-4612-5867-4 (ISBN)
1 Basic Properties of Hilbert Spaces.- 1.0 Introduction.- 1.1 Basic Definitions.- 1.2 Examples of Hilbert Spaces.- 1.3 Hilbert Spaces from Hilbert Spaces.- 1.4 Convex Sets and Projections.- 1.5 Orthogonality and Orthonormal Bases.- 1.6 Continuous Linear Functionals.- 1.7 Riesz Representation Theorem.- 1.8 Weak Convergence.- 1.9 Nonlinear Functionals and Generalized Curves.- 1.10 The Hahn-Banach Theorem.- 2 Convex Sets and Convex Programming.- 2.0 Introduction.- 2.1 Elementary Notions.- 2.2 Support Functional of a Convex Set.- 2.3 Minkowski Functional.- 2.4 The Support Mapping.- 2.5 Separation Theorem.- 2.6 Application to Convex Programming.- 2.7 Generalization to Infinite Dimensional Inequalities.- 2.8 A Fundamental Result of Game Theory: Minimax Theorem.- 2.9 Application: Theorem of Farkas.- 3 Functions, Transformations, Operators.- 3.0 Introduction.- 3.1 Linear Operators and their Adjoints.- 3.2 Spectral Theory of Operators.- 3.3 Spectral Theory of Compact Operators.- 3.4 Operators on Separable Hilbert Spaces.- 3.5 L2 Spaces over Hilbert Spaces.- 3.6 Multilinear Forms.- 3.7 Nonlinear Volterra Operators.- 4 Semigroups of Linear Operators.- 4.0 Introduction.- 4.1 Definitions and General Properties of Semigroups.- 4.2 Generation of Semigroups.- 4.3 Semigroups over Hilbert Spaces: Dissipative Semigroups.- 4.4 Compact Semigroups.- 4.5 Analytic (Holomorphic) Semigroups.- 4.6 Elementary Examples of Semigroups.- 4.7 Extensions.- 4.8 Differential Equations: Cauchy Problem.- 4.9 Controllability.- 4.10 State Reduction: Observability.- 4.11 Stability and Stabilizability.- 4.12 Boundary Input: An Example.- 4.13 Evolution Equations.- 5 Optimal Control Theory.- 5.0 Introduction.- 5.1 Preliminaries.- 5.2 Linear Quadratic Regulator Problem.- 5.3 Linear Quadratic Regulator Problem: Infinite Time Interval.- 5.4 Hard Constraints.- 5.5 Final Value Control.- 5.6 Time Optimal Control Problem.- 6 Stochastic Optimization Theory.- 6.0 Introduction.- 6.1 Preliminaries.- 6.2 Measures on Cylinder Sets.- 6.3 Characteristic Functions and Countable Additivity.- 6.4 Weak Random Variables.- 6.5 Random Variables.- 6.6 White Noise.- 6.7 Differential Systems.- 6.8 The Filtering Problem.- 6.9 Stochastic Control.- 6.10 Physical Random Variables.- 6.11 Radon-Nikodym Derivatives.- 6.12 Nonlinear Stochastic Equations.
Reihe/Serie | Stochastic Modelling and Applied Probability ; 3 |
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Zusatzinfo | XIII, 373 p. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
ISBN-10 | 1-4612-5867-7 / 1461258677 |
ISBN-13 | 978-1-4612-5867-4 / 9781461258674 |
Zustand | Neuware |
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