Abstract
According to results established by DeLeeuw-Rudin-Wermer and by Forelli, all linear isometries of any Hardy space H p (p ⩾ 1, p ≠ = 2) on the open unit disc Δ of ℂ are represented by weighted composition operators defined by inner functions on Δ. After reviewing (and completing when p = ∞) some of those results, the present report deals with a characterization of periodic and almost periodic semigroups of linear isometries of H p .
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