PreprintCC BY-NC-ND 4.0arXiv
Invertible non-cyclic functions in the little Bloch space
Abstract
This paper presents a method for exhibiting functions F in the little Bloch space B0 which are invertible, in the sense that 1/F also belongs to B0, and yet fail to be cyclic for the forward shift. The functions obtained in this way give rise to shift-invariant subspaces in B0 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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BibTeX
@misc{limani2026invertible,
title = {{Invertible non-cyclic functions in the little Bloch space}},
author = {Adem Limani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26318},
eprint = {2610.26318},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26318},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Invertible non-cyclic functions in the little Bloch space
AU - Adem Limani
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26318
UR - https://arxiv.org/abs/2610.26318
AB - 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.
ER -