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Analytic Continuation, Singular Value Expansions, and Kramers-Kronig Analysis



Andrew M. Dienstfrey, L Greengard


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.
Inverse Problems


analysis, analytic continuation, casusality, Hilbert transform, Krqamers-Kronig, singular value expansions


Dienstfrey, A. and Greengard, L. (2001), Analytic Continuation, Singular Value Expansions, and Kramers-Kronig Analysis, Inverse Problems, [online], (Accessed May 22, 2024)


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Created January 17, 2001, Updated February 19, 2017