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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Metric Geometry we must begin with the length of paths as the primary notion. From this, we will derive a distance function. More precisely, we can introduce a new distance which is measured along the shortest path between two points in a space (as opposed to simply measuring the Euclidean distance between the two

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Analytic Methods for Inverse Scattering Theoryering problems for time harmonic acoustic and Schr?dinger equations. Section 1 describes these two problems. In Section 2 we introduce the Hardy-Littlewood maximal function and define the Sobolev spaces in ?.. At the end of this Section we prove an important characterization of .. (?.) due to P. Haj

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Ray Transform on Riemannian Manifolds function or a more general object (cohomology class, tensor field, etc.) on a manifold, given its integrals over submanifolds of a prescribed class. In these lectures we only consider integral geometry problems for which the above-mentioned submanifolds are one-dimensional. Strictly speaking, the l

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Asymptotic Properties of Solutions to 3-particle Schr?dinger Equationsons of (. ? λ). = 0 in the Agmon-H?rmander space .* as the image of. .(λ)*. These stationary solutions admit asymptotic expansions in .* in terms of spherical waves associated with scattering channels.

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