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Binary dimension-free discretization and polynomial complexification on real cubes
Abstract
Let C(d,2) be the optimal dimension-free ratio between the polytorus and Boolean-cube norms of complex multiaffine polynomials of degree at most d. For every d, C(d,2) equals the unrestricted complexification constant of the real cube for complex polynomials of degree at most d. Moreover, limd→∞C(d,2)1/d=1+√2, and for every d≥3, β(1−6/(5d))(1+√2)d≤ C(d,2)≤(1+√2)d, where β=15π/[2(5√(26)+log(5+√(26)))]=0.8473222863….
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BibTeX
@misc{castanomarin2026binary,
title = {{Binary dimension-free discretization and polynomial complexification on real cubes}},
author = {Luis Miguel Castaño-Marín and Daniel Núñez-Alarcón and Joedson Santos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30587},
eprint = {2609.30587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30587},
}
RIS
TY - UNPB
TI - Binary dimension-free discretization and polynomial complexification on real cubes
AU - Luis Miguel Castaño-Marín
AU - Daniel Núñez-Alarcón
AU - Joedson Santos
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30587
UR - https://arxiv.org/abs/2609.30587
AB - Let C(d,2) be the optimal dimension-free ratio between the polytorus and Boolean-cube norms of complex multiaffine polynomials of degree at most d. For every d, C(d,2) equals the unrestricted complexification constant of the real cube for complex polynomials of degree at most d. Moreover, lim_d→∞C(d,2)^1/d=1+√2, and for every d≥3, β(1−6/(5d))(1+√2)^d≤ C(d,2)≤(1+√2)^d, where β=15π/[2(5√(26)+log(5+√(26)))]=0.8473222863….
ER -