Factors of Hypercontractions

TL;DR

This paper investigates contractive factors of m-hypercontractions, providing a characterization and explicit dilation on weighted Bergman spaces, extending previous research in the field.

Contribution

It introduces a new characterization of contractive factors of m-hypercontractions and constructs explicit dilations on weighted Bergman spaces, generalizing prior work.

Findings

Characterization of contractive factors of m-hypercontractions

Explicit dilation construction on weighted Bergman spaces

Extension of previous theoretical results

Abstract

In this article, we study a class of contractive factors of $m$-hypercontractions for $m \in \mathbb{N}$. We find a characterization of such factors and this is achieved by finding explicit dilation of these factors on some weighted Bergman spaces. This is a generalization of the work done in [14].