PreprintCC BY-NC-SA 4.0arXiv
On product spectral sets and functional tiles in ℚpd
Abstract
This paper studies product spectral sets and functional tiles in the p-adic spaces ℚpd within the framework of the {\bf product spectral set conjecture}. We establish a stability result for functional tiles under weak convergence of tiling complements, characterize product spectral pairs with product spectra, and fully resolve the conjecture for cylindric sets by proving that spectrality of a cylindric set Ω=Bγ(a)×Θ is equivalent to spectrality of Θ.
Versions
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BibTeX
@misc{kadir2026product,
title = {{On product spectral sets and functional tiles in $\mathbbQ_p^d$}},
author = {Mamateli Kadir},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22089},
eprint = {2609.22089},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22089},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - On product spectral sets and functional tiles in ℚ_p^d
AU - Mamateli Kadir
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.22089
UR - https://arxiv.org/abs/2609.22089
AB - This paper studies product spectral sets and functional tiles in the p-adic spaces ℚ_p^d within the framework of the {\bf product spectral set conjecture}. We establish a stability result for functional tiles under weak convergence of tiling complements, characterize product spectral pairs with product spectra, and fully resolve the conjecture for cylindric sets by proving that spectrality of a cylindric set Ω=B_γ(a)×Θ is equivalent to spectrality of Θ.
ER -