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Chuaqui, M., & Hernandez, R. (2013). The order of a linearly invariant family in C-n. J. Math. Anal. Appl., 398(1), 372–379.
Abstract: We study the (trace) order of the linearly invariant family in the ball B-n defined by parallel to SF parallel to <= alpha, where F : B-n -> C-n is locally biholomorphic and SF is the Schwarzian operator. By adapting Pommerenke's approach, we establish a characteristic equation for the extremal mapping that yields an upper bound for the order of the family in terms of alpha and the dimension n. Lower bounds for the order are established in similar terms by means of examples. (C) 2012 Elsevier Inc. All rights reserved.