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ON SOME HOLOMORPHIC DYNAMICAL SYSTEMS

1988
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Quarterly Journal of Mathematics
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Let D be a domain in C N and ϕ a holomorphic automorphism of D. Let C be the measure class of the Lebesgue measure in D, i.e., the set of all positive regular Borel measures on D whose null sets coincide with the Lebesgue null sets. Let ϕ * be the automorphism of C given by where B(D) denotes the Borel σ-algebra of D. Adopting the terminology introduced in [4], we will say that ϕ * is finite if it has a fixed point among probability measures. Let L 2 H(D) be the Hilbert space of all square

doi:10.1093/qmath/39.2.159
fatcat:vhywi7gwercifm4m4ur4wayvdy