On uniformly bounded basis in spaces of holomorphic functions

TL;DR

This paper constructs explicit uniformly bounded bases in spaces of complex homogeneous polynomials on the unit ball of C^3, extending previous work from C^2, and advancing understanding of basis structures in holomorphic function spaces.

Contribution

The paper introduces a new explicit construction of uniformly bounded bases in spaces of holomorphic functions on C^3, extending prior results from C^2.

Findings

Explicit uniformly bounded basis constructed for C^3 case

Extension of previous C^2 results to C^3

Advances understanding of basis properties in holomorphic function spaces

Abstract

The main result of the paper is the construction of explicit uniformly bounded basis in the spaces of complex homogenous polynomials on the unit ball of $C^3$, extending an earlier result of the author in the $C^2$ case