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arXiv · 2610.26318

Invertible non-cyclic functions in the little Bloch space

Adem Limani
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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.

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Adem Limani. 2026-10-19. Invertible non-cyclic functions in the little Bloch space. https://arxiv.org/abs/2610.26318

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