A few remarks about linear operators and disconnected open sets in the plane

TL;DR

This paper explores the properties of linear operators and the behavior of functions on disconnected open sets in the plane that have connected fractal boundaries, shedding light on their analytical characteristics.

Contribution

It provides new insights into the analysis of disconnected open subsets with fractal boundaries, an area with limited prior exploration.

Findings

Characterization of linear operators on fractal-boundary domains

Insights into function behavior on disconnected open sets

Potential applications in complex analysis and fractal geometry

Abstract

Some aspects of analysis on disconnected open subsets of the plane with connected fractal boundary are discussed.