Cantor sets and cyclicity in weighted Dirichlet spaces

TL;DR

This paper investigates the characterization of cyclic vectors in weighted Dirichlet spaces, extending previous results and developing new techniques due to the lack of a Carleson-type formula.

Contribution

It introduces novel methods to analyze cyclic vectors in weighted Dirichlet spaces, advancing understanding beyond classical cases.

Findings

Extended characterization of cyclic vectors in weighted Dirichlet spaces

Developed new techniques due to the absence of Carleson-type formulas

Generalized previous results from classical Dirichlet space

Abstract

We treat the problem of characterizing the cyclic vectors in the weighted Dirichlet spaces, extending some of our earlier results in the classical Dirichlet space. The absence of a Carleson-type formula for weighted Dirichlet integrals necessitates the introduction of new techniques.