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Composition operators: N α to the Bloch space to Q β

Jie Xiao (2000)

Studia Mathematica

Let N α ,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and Q β are Möbius invariant, but N α is not. We characterize, in function-theoretic terms, when the composition operator C ϕ f = f ϕ induced by an analytic self-map ϕ of the unit disk defines an operator C ϕ : N α B , B Q β , N α Q β which is bounded resp. compact.

Concave domains with trivial biholomorphic invariants

Witold Jarnicki, Nikolai Nikolov (2002)

Annales Polonici Mathematici

It is proved that if F is a convex closed set in ℂⁿ, n ≥2, containing at most one (n-1)-dimensional complex hyperplane, then the Kobayashi metric and the Lempert function of ℂⁿ∖ F identically vanish.

Concerning the energy class p for 0 < p < 1

Per Åhag, Rafał Czyż, Pham Hoàng Hiêp (2007)

Annales Polonici Mathematici

The energy class p is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of p and its pluricomplex p-energy is proved.

Conditions de régularité et éclatements

Jean-Pierre Henry, Michel Merle (1987)

Annales de l'institut Fourier

On décrit trois types de conditions permettant de stratifier un morphisme analytique complexe f  :1) différentielles, à la Thom-Whitney,2) géométriques, demandant l’équidimensionnalité de certains diviseurs exceptionnels obtenus à partir de l’espace conormal relatif ou de la modification de Nash relative de f ,3) numériques, exigeant la constance d’invariants de f le long des states.On donne une méthode générale permettant d’exprimer et de démontrer des équivalences entre des conditions de chaque...

Cône normal et régularités de Kuo-Verdier

Patrice Orro, David Trotman (2002)

Bulletin de la Société Mathématique de France

Nous introduisons de nouvelles régularités de Kuo-Verdier ( r e ) et montrons que pour une stratification C 2 ( a + r e ) ...

Conformal blocks and cohomology in genus 0

Prakash Belkale, Swarnava Mukhopadhyay (2014)

Annales de l’institut Fourier

We give a characterization of conformal blocks in terms of the singular cohomology of suitable smooth projective varieties, in genus 0 for classical Lie algebras and G 2 .

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