PreprintCC BY-NC-ND 4.0arXiv
When surjectivity demands pathology
Abstract
In this paper, we characterize surjective nonlinear composition operators acting between the space of sequences of bounded variation and the space of bounded sequences. We show that their generators exhibit highly pathological behavior. To complement this, we construct explicit examples, confirming that such exotic objects do in fact exist.
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BibTeX
@misc{kasprzak2026when,
title = {{When surjectivity demands pathology}},
author = {Piotr Kasprzak and Piotr Maćkowiak},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10837},
eprint = {2610.10837},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10837},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - When surjectivity demands pathology
AU - Piotr Kasprzak
AU - Piotr Maćkowiak
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10837
UR - https://arxiv.org/abs/2610.10837
AB - In this paper, we characterize surjective nonlinear composition operators acting between the space of sequences of bounded variation and the space of bounded sequences. We show that their generators exhibit highly pathological behavior. To complement this, we construct explicit examples, confirming that such exotic objects do in fact exist.
ER -