Functional Analysis
Springer (Verlag)
978-0-7923-3849-9 (ISBN)
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1 Introduction.- 1.1 Real and complex numbers.- 1.2 Theory of functions.- 1.3 Weierstrass’ polynomial approximation theorem.- 2 Introduction to Metric Spaces.- 2.1 Preliminaries.- 2.2 Sets in a metric space.- 2.3 Some metric spaces of functions.- 2.4 Convergence in a metric space.- 2.5 Complete metric spaces.- 2.6 The completion theorem.- 2.7 An introduction to operators.- 2.8 Normed linear spaces.- 2.9 An introduction to linear operators.- 2.10 Some inequalities.- 2.11 Lebesgue spaces.- 2.12 Inner product spaces.- 3 Energy Spaces and Generalized Solutions.- 3.1 The rod.- 3.2 The Euler-Bernoulli beam.- 3.3 The membrane.- 3.4 The plate in bending.- 3.5 Linear elasticity.- 3.6 Sobolev spaces.- 3.7 Some imbedding theorems.- 4 Approximation in a Normed Linear Space.- 4.1 Separable spaces.- 4.2 Theory of approximation in a normed linear space.- 4.3 Riesz’s representation theorem.- 4.4 Existence of energy solutions of some mechanics problems.- 4.5 Bases and complete systems.- 4.6 Weak convergence in a Hilbert space.- 4.7 Introduction to the concept of a compact set.- 4.8 Ritz approximation in a Hilbert space.- 4.9 Generalized solutions of evolution problems.- 5 Elements of the Theory of Linear Operators.- 5.1 Spaces of linear operators.- 5.2 The Banach-Steinhaus theorem.- 5.3 The inverse operator.- 5.4 Closed operators.- 5.5 The adjoint operator.- 5.6 Examples of adjoint operators.- 6 Compactness and Its Consequences.- 6.1 Sequentially compact ? compact.- 6.2 Criteria for compactness.- 6.3 The Arzela-Ascoli theorem.- 6.4 Applications of the Arzela-Ascoli theorem.- 6.5 Compact linear operators in normed linear spaces.- 6.6 Compact linear operators between Hilbert spaces.- 7 Spectral Theory of Linear Operators.- 7.1 The spectrum of a linear operator.- 7.2 The resolventset of a closed linear operator.- 7.3 The spectrum of a compact linear operator in a Hilbert space.- 7.4 The analytic nature of the resolvent of a compact linear operator.- 7.5 Self-adjoint operators in a Hilbert space.- 8 Applications to Inverse Problems.- 8.1 Well-posed and ill-posed problems.- 8.2 The operator equation.- 8.3 Singular value decomposition.- 8.4 Regularization.- 8.5 Morozov’s discrepancy principle.
Erscheint lt. Verlag | 29.2.1996 |
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Reihe/Serie | Solid Mechanics and Its Applications ; 41 |
Zusatzinfo | VIII, 248 p. |
Verlagsort | Dordrecht |
Sprache | englisch |
Maße | 160 x 240 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
Technik ► Maschinenbau | |
ISBN-10 | 0-7923-3849-9 / 0792338499 |
ISBN-13 | 978-0-7923-3849-9 / 9780792338499 |
Zustand | Neuware |
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