Functional analysis : applications in mechanics and inverse problems

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Functional analysis : applications in mechanics and inverse problems / by L.P. Lebedev, I.I. Vorovich and G.M.L. Gladwell

版:

2nd ed

資料種別:

図書

出版情報:

Dordrecht : Kluwer Academic, c2002

形態:

x, 247 p. ; 25 cm

シリーズ名:

Solid mechanics and its applications ; v. 100 <BA08040895>

著者名:

ISBN:

9781402006678 [1402006675]
9781402007569 [1402007566] (: pbk)

書誌ID:

BA57726961

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes index

主題:

Functional analysis

言語:

英語

目次情報:

Introduction / 1：

Real and complex numbers / 1.1：

Theory of functions / 1.2：

Weierstrass' polynomial approximation theorem / 1.3：

Introduction to Metric Spaces / 2：

Preliminaries / 2.1：

Sets in a metric space / 2.2：

Some metric spaces of functions / 2.3：

Convergence in a metric space / 2.4：

Complete metric spaces / 2.5：

The completion theorem / 2.6：

An introduction to operators / 2.7：

Normed linear spaces / 2.8：

An introduction to linear operators / 2.9：

Some inequalities / 2.10：

Lebesgue spaces / 2.11：

Inner product spaces / 2.12：

Energy Spaces and Generalized Solutions / 3：

The rod / 3.1：

The Euler-Bernoulli beam / 3.2：

The membrane / 3.3：

The plate in bending / 3.4：

Linear elasticity / 3.5：

Sobolev spaces / 3.6：

Some imbedding theorems / 3.7：

Approximation in a Normed Linear Space / 4：

Separable spaces / 4.1：

Theory of approximation in a normed linear space / 4.2：

Riesz's representation theorem / 4.3：

Existence of energy solutions of some mechanics problems / 4.4：

Bases and complete systems / 4.5：

Weak convergence in a Hilbert space / 4.6：

Introduction to the concept of a compact set / 4.7：

Ritz approximation in a Hilbert space / 4.8：

Generalized solutions of evolution problems / 4.9：

Elements of the Theory of Linear Operators / 5：

Spaces of linear operators / 5.1：

The Banach-Steinhaus theorem / 5.2：

The inverse operator / 5.3：

Closed operators / 5.4：

The adjoint operator / 5.5：

Examples of adjoint operators / 5.6：

Compactness and Its Consequences / 6：

Sequentially compact [identical with] compact / 6.1：

Criteria for compactness / 6.2：

The Arzela-Ascoli theorem / 6.3：

Applications of the Arzela-Ascoli theorem / 6.4：

Compact linear operators in normed linear spaces / 6.5：

Compact linear operators between Hilbert spaces / 6.6：

Spectral Theory of Linear Operators / 7：

The spectrum of a linear operator / 7.1：

The resolvent set of a closed linear operator / 7.2：

The spectrum of a compact linear operator in a Hilbert space / 7.3：

The analytic nature of the resolvent of a compact linear operator / 7.4：

Self-adjoint operators in a Hilbert space / 7.5：

Applications to Inverse Problems / 8：

Well-posed and ill-posed problems / 8.1：

The operator equation / 8.2：

Singular value decomposition / 8.3：

Regularization / 8.4：

Morozov's discrepancy principle / 8.5：

Index

Introduction / 1：

Real and complex numbers / 1.1：

Theory of functions / 1.2：

Weierstrass' polynomial approximation theorem / 1.3：

Introduction to Metric Spaces / 2：

Preliminaries / 2.1：

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