Remote temperature sensing in 2D and the Bergman kernel

TL;DR

This paper investigates estimating the steady state temperature at a point in a 2D domain using high-order temperature data at another point, revealing connections to complex analysis concepts like the Bergman kernel.

Contribution

It introduces a novel approach linking temperature estimation to the Bergman kernel, Runge's theorem, and null quadrature identities in complex analysis.

Findings

Established a theoretical connection between temperature estimation and the Bergman kernel.

Derived implications of Runge's theorem for temperature sensing.

Linked approximate null quadrature identities to temperature measurement accuracy.

Abstract

We explore the problem of estimating the steady state temperature in a two-dimensional domain at a point knowing the temperature to high order at another point. We find connections to the Bergman kernel of the domain, Runge's theorem, and approximate null quadrature identities.