Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

1. Front Matter

   Pages N2-viii

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2. Introduction

   • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

   Pages 1-3

3. 1. Mathematical preliminaries

   • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

   Pages 5-16

4. 2. Regularization of moment problems by truncated expansion and by the Tikhonov method

   • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

   Pages 17-49

5. 3. Backus-Gilbert regularization of a moment problem

   • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

   Pages 51-81

6. 4. The Hausdorff moment problem: regularization and error estimates

   • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

   Pages 83-97

7. 5. Analytic functions: reconstruction and Sinc approximations

   • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

   Pages 99-130

8. 6. Regularization of some inverse problems in potential theory

   • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

   Pages 131-146

9. 7. Regularization of some inverse problems in heat conduction

   • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

   Pages 147-169

10. 8. Epilogue

    • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

    Pages 171-173

11. References

    • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

    Pages 175-180

12. Index

    • Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong

    Pages 181-183

13. Back Matter

    Pages 185-185

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Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations.

• Moment problems
• Potential theory
• inverse problems
• partial differential equation
• reconstruction of analytic functions
• regularization methods
• partial differential equations

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