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1997 | 66 | 1 | 239-252
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Analytic formulas for the hyperbolic distance between two contractions

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In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes as values strict contractions.
  • Institute of Mathematics, Romanian Academy, P.O. Box 1-764, RO-70700, Bucharest, Romania
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