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Titlebook: New Analytic and Geometric Methods in Inverse Problems; Lectures given at th Kenrick Bingham,Yaroslav V. Kurylev,Erkki Somersal Book 2004 S

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978-3-642-07379-3Springer-Verlag Berlin Heidelberg 2004
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Intertwining Operators in Inverse Scatteringheory on the real line for the Schrödinger operator. These methods are based on the construction of operators intertwining the Schrödinger operator with the ‘free operator’ obtained when the potential term is removed. We refer to the monograph [5] by V. A. Marchenko and to the paper [6] for a detailed presentation of this technique.
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Uniqueness in Inverse Obstacle Scatteringng of time-harmonic acoustic or electromagnetic waves. We will review and outline different methods for proving global and local uniqueness theorems for impenetrable and penetrable obstacles. In addition, we will draw attention to open uniqueness problems in inverse obstacle scattering.
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Geometric Methods for Anisotopic Inverse Boundary Value Problemsld of the domain. Differential forms arise as the natural objects to integrate over submanifolds of each dimension. We will see that the (possibly anisotropic) material response to a field can be naturally associated with a Hodge star operator.
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