arXiv 1402.46412014-02-19math-phmath.MP

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

G. N. Makrakis

英文摘要：

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

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