Extrapolation, a technique to estimate

TL;DR

This paper presents a novel extrapolation technique for estimating linear operators by embedding them into a family with specific curvature properties, enabling norm estimation through limiting bounds, demonstrated on a complex geometry extension problem.

Contribution

Introduces a new extrapolation method for linear operators using operator families with curvature properties, applicable to complex geometry extension problems.

Findings

Effective estimation of operator norms via limits

Application to complex geometry extension problems

Potential for broader applications in analysis

Abstract

We introduce a technique to estimate a linear operator by embedding it in a family $A_t$ of operators, $t\in(\sigma_0,\infty)$, with suitable curvature properties. One can then estimate the norm of each $A_t$ by bounds that hold in the limit $t\to\sigma_0$, respectively, $t\to\infty$. We illustrate this technique on an extension problem that arises in complex geometry.