| 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: |
 Click here to retrieve PDF version of paper (238KB) |
