Year: 2026
Type: preprint
Abstract: The existence of independent inner functions is established: there exist inner functions $φ$ and $ψ$, both vanishing at the origin, such that $$ \frac{1}{2π}\int_0^{2π} φ^m(e^{iθ}) \overline{ψ^n(e^{iθ})}\,dθ= 0, \qquad m,n \geq 1. $$ 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.
Source: arXiv (Cornell University)
Authors: Fu, Xiangdi, Guo, Kunyu, Li, Dilong, Qiu, Yanqi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5391795570
OpenAlex ID: W7223216096