### 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 language | English (US) |
---|---|

Pages (from-to) | 1307-1320 |

Number of pages | 14 |

Journal | Inverse Problems |

Volume | 17 |

Issue number | 5 |

DOIs | |

State | Published - Oct 2001 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Inverse Problems*,

*17*(5), 1307-1320. https://doi.org/10.1088/0266-5611/17/5/305

**Analytic continuation, singular-value expansions, and Kramers-Kronig analysis.** / Dienstfrey, A.; Greengard, Leslie.

Research output: Contribution to journal › Article

*Inverse Problems*, vol. 17, no. 5, pp. 1307-1320. https://doi.org/10.1088/0266-5611/17/5/305

}

TY - JOUR

T1 - Analytic continuation, singular-value expansions, and Kramers-Kronig analysis

AU - Dienstfrey, A.

AU - Greengard, Leslie

PY - 2001/10

Y1 - 2001/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035472967&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035472967&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/17/5/305

DO - 10.1088/0266-5611/17/5/305

M3 - Article

AN - SCOPUS:0035472967

VL - 17

SP - 1307

EP - 1320

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 5

ER -