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This talk will discuss how to study singular rational inner functions (RIFs) using their zero set behaviors. In the two-variable setting, zero sets can be used to define a quantity called contact order, which helps quantify derivative integrability and non-tangential regularity. In the three-variable and higher setting, the RIF singular sets (and corresponding zero sets) can be much more complicated. We will discuss what holds in general, what holds for simple three-variable RIFs, and some examples illustrating why some of the nice two-variable behavior is lost in higher dimensions. This is joint work with James Pascoe and Alan Sola.
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This talk will discuss how to study singular rational inner functions (RIFs) using their zero set behaviors. In the two-variable setting, zero sets can be used to define a quantity called contact order, which helps quantify derivative integrability and non-tangential regularity. In the three-variable and higher setting, the RIF singular sets (and corresponding zero sets) can be much more complicated. We will discuss what holds in general, ...
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32A20 ; 14C17 ; 14H20 ; 32A35 ; 32A40