Moment theory and some inverse problems in potential theory and heat conduction

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Moment theory and some inverse problems in potential theory and heat conduction / Dang Dinh Ang ... [et al.]

資料種別:: 図書
出版情報:: Berlin ; Tokyo : Springer, c2002
形態:: viii, 183 p. ; 24 cm
シリーズ名:: Lecture notes in mathematics ; 1792 <BA00146586>
著者名:: Ang, Dang Dinh <DA13730811>
ISBN:: 9783540440062 [3540440062]
書誌ID:: BA5879596X

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注記:

Bibliography: p. [175]-180
Includes index

言語:

英語

目次情報:

Introduction

Mathematical preliminaries / 1：

Banach spaces / 1.1：

Hilbert spaces / 1.2：

Some useful function spaces / 1.3：

Spaces of continuous functions / 1.3.1：

Spaces of integrable functions / 1.3.2：

Sobolev spaces / 1.3.3：

Analytic functions and harmonic functions / 1.4：

Fourier transform and Laplace transform / 1.5：

Regularization of moment problems by truncated expansion and by the Tikhonov method / 2：

Method of truncated expansion / 2.1：

A construction of regularized solutions / 2.1.1：

Convergence of regularized solutions and error estimates / 2.1.2：

Error estimates using eigenvalues of the Laplacian / 2.1.3：

Method of Tikhonov / 2.2：

Case 1: exact solutions in L²(Ω) / 2.2.1：

Case 2: exact solutions in L^α* (Ω), 1 < α^&infinity; < 8 / 2.2.2：

Case 3: exact solutions in H¹(Ω) / 2.2.3：

Notes and remarks / 2.3：

Backus-Gilbert regularization of a moment problem / 3：

Backus-Gilbert solutions and their stability / 3.1：

Definition of the Backus-Gilbert solutions / 3.2.1：

Stability of the Backus-Gilbert solutions / 3.2.2：

Regularization via Backus-Gilbert solutions / 3.3：

Definitions and notations / 3.3.1：

Main results / 3.3.2：

The Hausdorff moment problem: regularization and error estimates / 4：

Finite moment approximation of (4.1) / 4.1：

Proof of Theorem 4.1 / 4.1.1：

Proof of Theorem 4.2 / 4.1.2：

A moment problem from Laplace transform / 4.2：

Analytic functions: reconstruction and Sinc approximations / 4.3：

Reconstruction of functions in H²(U): approximation by polynomials / 5.1：

Reconstruction of an analytic function: a problem of optimal recovery / 5.2：

Cardinal series representation and approximation: reformulation of moment problems / 5.3：

Two-dimensional Sinc theory / 5.3.1：

Approximation theorems / 5.3.2：

Regularization of some inverse problems in potential theory / 6：

Analyticity of harmonic functions / 6.1：

CauchyÆs problem for the Laplace equation / 6.2：

Surface temperature determination from borehole measurements (steady case) / 6.3：

Regularization of some inverse problems in heat conduction147 / 7：

The backward heat equation / 7.1：

Surface temperature determination from borehole measurements: a two-dimensional problem / 7.2：

An inverse two-dimensional Stefan problem: identification of boundary values / 7.3：

Epilogue / 7.4：

References

Index

Introduction

Mathematical preliminaries / 1：

Banach spaces / 1.1：

Hilbert spaces / 1.2：

Some useful function spaces / 1.3：

Spaces of continuous functions / 1.3.1：

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