Sur les équations aux intégrales réciproques
Commuting multi-contractions of class and having a regular isometric dilation are studied. We prove that a polydisc contraction of class is the restriction of a backwards multi-shift to an invariant subspace, extending a particular case of a result by R. E. Curto and F.-H. Vasilescu. A new condition on a commuting multi-operator, which is equivalent to the existence of a regular isometric dilation and improves a recent result of A. Olofsson, is obtained as a consequence.
Let be a psh function on a bounded pseudoconvex open set , and let be the associated multiplier ideal sheaves, . Motivated by global geometric issues, we establish an effective version of the coherence property of as . Namely, given any , we estimate the asymptotic growth rate in of the number of generators of over , as well as the growth of the coefficients of sections in with respect to finitely many generators globally defined on . Our approach relies on proving asymptotic integral...
Let J be the Julia set of a conformal dynamics f. Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out to be equivalent to the existence of a conformal change of variable which reduces the dynamical system...
Page 1