Analytic continuation, singular-value expansions, and Kramers-Kronig analysis

A. Dienstfrey, L. Greengard

Research output: Contribution to journalArticlepeer-review

Abstract

We describe a systematic approach to the recovery of a function analytic in the upper half-plane, C+, from measurements over a finite interval on the real axis, D ⊂ R. Analytic continuation problems of this type are well known to be 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 measurement window D itself. The resulting procedure is robust in the presence of noise, and we demonstrate its performance with some numerical experiments.

Original languageEnglish (US)
Pages (from-to)1307-1320
Number of pages14
JournalInverse Problems
Volume17
Issue number5
DOIs
StatePublished - Oct 2001

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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