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On the existence of independent inner functions
Abstract
The existence of independent inner functions is established: there exist inner functions φ and ψ, both vanishing at the origin, such that 1/2π∫02π φm(eiθ) ψn(eiθ)̅ dθ= 0, m,n ≥ 1. In fact, both φ and ψ can be chosen to be Blaschke products. The proof proceeds by an iterative construction, which suggests a general approach to produce inner functions with a desired joint distribution.
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BibTeX
@misc{fu2026existence,
title = {{On the existence of independent inner functions}},
author = {Xiangdi Fu and Kunyu Guo and Dilong Li and Yanqi Qiu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29198},
eprint = {2610.29198},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29198},
}
RIS
TY - UNPB
TI - On the existence of independent inner functions
AU - Xiangdi Fu
AU - Kunyu Guo
AU - Dilong Li
AU - Yanqi Qiu
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29198
UR - https://arxiv.org/abs/2610.29198
AB - The existence of independent inner functions is established: there exist inner functions φ and ψ, both vanishing at the origin, such that 1/2π∫_0^2π φ^m(e^iθ) ψ^n(e^iθ)̅ dθ= 0, m,n ≥ 1. In fact, both φ and ψ can be chosen to be Blaschke products. The proof proceeds by an iterative construction, which suggests a general approach to produce inner functions with a desired joint distribution.
ER -