Abstract
In contrast with the one-variable case, there is a large number of distinct submodules of the Hardy module over the polydisk algebra in the multi-variable use. We show that under hypotheses on the zero sets, two submodules which are equivalent in any reasonable sense must be equal. This is the rigidity referred to in the title.
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The research of the first author was partially supported by a grant from the National Science Foundation.
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Douglas, R.G., Yan, K. On the rigidity of Hardy submodules. Integr equ oper theory 13, 350–363 (1990). https://doi.org/10.1007/BF01199890
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DOI: https://doi.org/10.1007/BF01199890