Rotational symmetries of domains and orthogonality relations

Soumya Ganguly; John N. Treuer

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arXiv · 2410.01115

Rotational symmetries of domains and orthogonality relations

Soumya Ganguly·John N. Treuer

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Abstract

Let $\Omega \subset \mathbb{C}^n$ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for $\Omega$ to be Reinhardt, complete Reinhardt, circular or Hartogs in terms of the orthogonality relations of the monomials with respect to their $L^2$-inner products and their $L^2$-norms. More generally, we give sufficient conditions for $\Omega$ to be invariant under a linear group action of an $r$-dimensional torus, where $r \in \{1,\ldots, n\}$.

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Soumya Ganguly, John N. Treuer. 2024-10-01. Rotational symmetries of domains and orthogonality relations. https://arxiv.org/abs/2410.01115

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