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On C 0 · multi-contractions having a regular dilation

Dan Popovici — 2005

Studia Mathematica

Commuting multi-contractions of class C 0 · and having a regular isometric dilation are studied. We prove that a polydisc contraction of class C 0 · 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.

Effective local finite generation of multiplier ideal sheaves

Dan Popovici — 2010

Annales de l’institut Fourier

Let ϕ be a psh function on a bounded pseudoconvex open set Ω n , and let ( m ϕ ) be the associated multiplier ideal sheaves, m . Motivated by global geometric issues, we establish an effective version of the coherence property of ( m ϕ ) as m + . Namely, given any B Ω , we estimate the asymptotic growth rate in m of the number of generators of ( m ϕ ) | B over 𝒪 Ω , as well as the growth of the coefficients of sections in Γ ( B , ( m ϕ ) ) with respect to finitely many generators globally defined on Ω . Our approach relies on proving asymptotic integral...

Rigidity of harmonic measure

I. PopoviciAlexander Volberg — 1996

Fundamenta Mathematicae

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...

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