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New Analytic and Geometric Methods in Inverse Problems : Lectures given at the EMS Summer School and Conference held in Edinburgh, Scotland 2000

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In inverse problems, the aim is to obtain, via a mathematical model, information on quantities that are not directly observable but rather depend on other observable quantities. Inverse problems are encountered in such diverse areas of application as medical imaging, remote sensing, material testing, geosciences and financing. It has become evident that new ideas coming from differential geometry and modern analysis  Read more...

Abstract:
In inverse problems, the aim is to obtain, via a mathematical model, information on quantities that are not directly observable but rather depend on other observable quantities. Inverse problems are  Read more...

Author(s): Bingham, Kenrick; Kurylev, Yaroslav V.; Somersalo, Erkki (eds.)
Publisher: Springer Berlin Heidelberg
Year: 2004

Language: English
Pages: 381
City: Berlin, Heidelberg
Tags: Mathematics.;Differential equations, Partial.;Global differential geometry.;Analysis.;Partial Differential Equations.;Differential Geometry.

Content: I. EMS Summer School: New Analytic and Geometric Methods in Inverse Problems --
Metric Geometry --
Intertwining Operators in Inverse Scattering --
Carleman Type Estimates and Their Applications --
Gaussian Beams and Inverse Boundary Spectral Problems --
Analytic Methods for Inverse Scattering Theory --
Ray Transform on Riemannian Manifolds --
On the Local Dirichlet-to-Neumann Map --
II. EMS Conference: Recent Developments in the Wave Field and Diffuse Tomographic Inverse Problems --
Remarks on the Inverse Scattering Problem for Acoustic Waves --
Asymptotic Properties of Solutions to 3-particle Schrödinger Equations --
Stability and Reconstruction in Gel'fand Inverse Boundary Spectral Problem --
Uniqueness in Inverse Obstacle Scattering --
Geometric Methods for Anisotopic Inverse Boundary Value Problems --
Applications of the Oscillating-Decaying Solutions to Inverse Problems --
Time-Dependent Methods in Inverse Scattering Theory.