On Embedding problem of linear fractional maps on the unit ball of $\mathbb{C}^{N}$

TL;DR

This paper investigates the conditions under which linear fractional maps on the unit ball in complex N-dimensional space can be embedded into semigroups of holomorphic self-maps, advancing understanding of their structural properties.

Contribution

It provides new criteria for when linear fractional maps can be embedded into semigroups of holomorphic self-maps on the unit ball in complex space.

Findings

Characterization of embedding conditions for linear fractional maps.

Identification of structural properties enabling embedding.

Extension of previous results to higher dimensions.

Abstract

This paper focuses on the embedding problem of linear fractional maps which explains when a linear fractional self-map of $B_{N}$ can be a member of a semigroup of holomorphic self-maps on the unit ball $B_{N}$ of the complex $N$-dimensional Euclidean space $\mathbb{C}^{N}$.