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

Published

Author(s)

Andrew M. Dienstfrey, L Greengard

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

Keywords

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

Citation

Dienstfrey, A. and Greengard, L. (2001), Analytic Continuation, Singular Value Expansions, and Kramers-Kronig Analysis, Inverse Problems, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150820 (Accessed May 22, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created January 17, 2001, Updated February 19, 2017