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Isometric rigidity of complete Pick algebras on monomial varieties
Abstract
We establish a geometric rigidity theorem for a class of monomial varieties in finite-dimensional unit balls. Every ball automorphism mapping one such variety onto another is unitary, and whenever such an equivalence exists, it can also be realized by a permutation of the ambient coordinates. As a consequence, we obtain a complete isometric classification of the multiplier algebras of integrally generated complete Nevanlinna--Pick Dirichlet series kernels in terms of their defining weight and frequency data. We also obtain an explicit isometric classification for a class of complete Nevanlinna--Pick kernels on bounded Reinhardt domains.
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BibTeX
@misc{ahmed2026isometric,
title = {{Isometric rigidity of complete Pick algebras on monomial varieties}},
author = {Hamidul Ahmed and B. Krishna Das and Chaman Kumar Sahu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10765},
eprint = {2610.10765},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10765},
}
RIS
TY - UNPB
TI - Isometric rigidity of complete Pick algebras on monomial varieties
AU - Hamidul Ahmed
AU - B. Krishna Das
AU - Chaman Kumar Sahu
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10765
UR - https://arxiv.org/abs/2610.10765
AB - We establish a geometric rigidity theorem for a class of monomial varieties in finite-dimensional unit balls. Every ball automorphism mapping one such variety onto another is unitary, and whenever such an equivalence exists, it can also be realized by a permutation of the ambient coordinates. As a consequence, we obtain a complete isometric classification of the multiplier algebras of integrally generated complete Nevanlinna--Pick Dirichlet series kernels in terms of their defining weight and frequency data. We also obtain an explicit isometric classification for a class of complete Nevanlinna--Pick kernels on bounded Reinhardt domains.
ER -