Formal asymptotic expansion of the Faddeev-Green function in unbounded domains

2014/02/19 by George N. Makrakis, Makrakis, G. N.
Mathematics · Computer Science · Engineering · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Microwave Imaging and Scattering Analysis

paper · pdf · doi:10.48550/arxiv.1402.4641

Abstract

We consider the Faddeev-Green function in the three-dimensional space and in a slab, and we construct formal asymptotic expansions for the large complex parameter appearing in this function. The basic idea of the construction is to express the Faddeev-Green function through the standard exponential integral and to use the standard asymptotic expansion of this special function. In the three-dimensional space, the constructed expansion of the Faddeev-Green function clearly suggests the form of the rigorous estimate proved by Sylvester and Uhlmann. and which is the basis of complex-geometric optics' techniques in inverse problems. A similar estimate is suggested for the slab case

Citations

• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

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