Rational inner functions on the bidisk belong to the studied Dirichlet spaces precisely when their contact order at singular points satisfies a threshold condition.
Pascoe,A wedge-of-the-edge theorem: analytic continuation of multivariable Pick functions in and around the boundary, Bull
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On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type
Rational inner functions on the bidisk belong to the studied Dirichlet spaces precisely when their contact order at singular points satisfies a threshold condition.