Rotational symmetries of domains and orthogonality relations

2024/10/01 by Ganguly, Soumya, Treuer, John N.
#32A36 #32Q06 #44A60 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.01115

Abstract

Let Ω⊂ ℂⁿ be a domain whose Bergman space contains all holomorphic monomials. We derive sufficient conditions for Ω to be Reinhardt, complete Reinhardt, circular or Hartogs in terms of the orthogonality relations of the monomials with respect to their L²-inner products and their L²-norms. More generally, we give sufficient conditions for Ω to be invariant under a linear group action of an r-dimensional torus, where r ∈ \1,…, n\.

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