Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: Indian Institute of Technology Bombay
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221078022