On structure of $L^2$-harmonic functions for one-dimensional diffusions

TL;DR

This paper investigates the structure of harmonic functions in the $L^2$-sense for one-dimensional irreducible diffusions, providing insights into their mathematical properties and potential applications.

Contribution

It offers a novel analysis of $L^2$-harmonic functions specific to one-dimensional diffusions, expanding understanding of their structure and behavior.

Findings

Characterization of $L^2$-harmonic functions for diffusions

Identification of conditions for harmonic function existence

Insights into the mathematical structure of these functions

Abstract

In this note we analyse the harmonic functions in $L^2$-sense for an irreducible diffusion on an interval.