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Publication Citation: Analytic Continuation, Singular Value Expansions, and Kramers-Kronig Analysis

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Author(s): Andrew M. Dienstfrey; L Greengard;
Title: Analytic Continuation, Singular Value Expansions, and Kramers-Kronig Analysis
Published: January 17, 2001
Abstract: We describe a systematic approach to the recovery of a function analytic in the upper half plane, ${\bfC:^+$, from measurements over a finite interval on the real axis, $D\subset {\bfR}$. Analytic continuation problems of this type are well-known to ill-posed. Thus, the best one can hope for is a simple, linear procedure which exposes this underlying difficulty and solves the problem in a least squares sense to accomplish this, we first construct an explicit analytic approximation of the desired function and recast the continuation problem in terms of a residual function defined on the defined on the measurement window $D$ itself. The result procedure is robust in the presence of noise and we demonstrate its performance with some numerical experiments.
Citation: Inverse Problems
Volume: 17
Pages: pp. 1307 - 1320
Keywords: analysis,analytic continuation,casusality,Hilbert transform,Krqamers-Kronig,singular value expansions
Research Areas: Math
PDF version: PDF Document Click here to retrieve PDF version of paper (244KB)