An extension problem of higher order operators and operators of logarithmic type via renormalization

TL;DR

This paper develops a higher order extension method inspired by renormalization techniques and offers a new perspective on the extension problem for the logarithmic Laplacian, connecting advanced operator theories.

Contribution

It introduces a novel higher order extension approach using renormalization and provides an alternative view on the logarithmic Laplacian extension problem.

Findings

New higher order extension method via renormalization

Alternative perspective on logarithmic Laplacian extension

Connections between extension problems and advanced operator theories

Abstract

We introduce a method of obtaining a higher order extension problem, \'a la Caffarelli-Silvestre, utilizing ideas from renormalization. Moreover, we give an alternative perspective of the recently developed extension problem for the logarithmic laplacian developed by Chen, Hauer and Weth (2023) [arXiv:2312.15689].