Third-order agreement with a maximal Blaschke product along one non-tangential sequence forces a holomorphic self-map of the disk to equal that Blaschke product.
Abate.Holomorphic Dynamics on Hyperbolic Riemann Surfaces
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A Burns-Krantz type theorem for Blaschke products
Third-order agreement with a maximal Blaschke product along one non-tangential sequence forces a holomorphic self-map of the disk to equal that Blaschke product.