Year: 2026
Type: preprint
Abstract: This paper presents a method for exhibiting functions $F$ in the little Bloch space $\B_0$ which are invertible, in the sense that $1/F$ also belongs to $\B_0$, and yet fail to be cyclic for the forward shift. The functions obtained in this way give rise to shift-invariant subspaces in $\B_0$ of index two, of a special type. The approach rests on a harmonic-measure criterion for non-cyclicity. This criterion gives a new manifestation of a principle of Borichev and Hedenmalm, and applies in a broad class of spaces of analytic functions.
Source: arXiv (Cornell University)
Author: Limani, Adem
Institution: Lund University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223052303