On feasibility of extrapolation of the complex electromagnetic permittivity function using Kramer-Kronig relations

2020/09/25 by Yury Grabovsky, Grabovsky, Yury, Narek Hovsepyan +1 · 1 citation
Decision Sciences · Mathematics · #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Probabilistic and Robust Engineering Design #Scientific Measurement and Uncertainty Evaluation

paper · pdf · doi:10.48550/arxiv.2009.12441

openalex publication_date 2020/09/25 · openalex created_date 2020/10/01 · openalex updated_date 2026/07/28

Abstract

We study the degree of reliability of extrapolation of complex electromagnetic permittivity functions based on their analyticity properties. Given two analytic functions, representing extrapolants of the same experimental data, we examine how much they can differ at an extrapolation point outside of the experimentally accessible frequency band. We give a sharp upper bound on the worst case extrapolation error, in terms of a solution of an integral equation of Fredholm type. We conjecture and give numerical evidence that this bound exhibits a power law precision deterioration as one moves further away from the frequency band containing measurement data.

Citations

• On the Theory of Dispersion of X-Rays

Cited by

• On the optimal analytic continuation from discrete data

Related

• Kramers-Kronig relations and the properties of conductivity and\n permittivity in heterogeneous media
• Extracting the contribution of conduction in permittivity measurements using the Kramers-Kronig relations
• Analytic properties of the electromagnetic Green's function
• General Mapping between Complex Spatial and Temporal Frequencies by\n Analytical Continuation
• Imaginary part of the conductivity using Kramers-Kronig relations