Pascal J. Thomas

Weakly sufficient sets for A−∞(D)

In the space

Gromov (non-)hyperbolicity of certain domains in ℂN

A^{-\infty} (\Bbb D)

Discontinuity of the Lempert function of the spectral ball

of functions of polynomial growth, weakly sufficient sets are those such that the topology induced by restriction to the set coincides with the topology of the original space. Horowitz, Korenblum and Pinchuk defined sampling sets for

A local form for the automorphisms of the spectral unit ball

A^{-\infty} (\Bbb D)

On hyperbolicity and tautness modulo an analytic subset of Hartogs domains

as those such that the restriction of a function to the set determines the type of growth of the function. We show that sampling sets are always weakly sufficient, that weakly sufficient sets are always of uniqueness, and provide examples of discrete sets that show that the converse implications do not hold

LIMITS OF MULTIPOLE PLURICOMPLEX GREEN FUNCTIONS

Abstract We prove the Gromov non-hyperbolicity with respect to the Kobayashi distance for 𝒞 1 , 1

DECREASE OF BOUNDED HOLOMORPHIC FUNCTIONS ALONG DISCRETE SETS

{\mathcal{C}^{1,1}}

Powers of ideals and convergence of Green functions with colliding poles

-smooth convex domains in ℂ 2

Algebras generated by two bounded holomorphic functions

{\mathbb{C}^{2}}

Continuity and convergence properties of extremal-interpolating disks

which contain an analytic disc in the boundary or have a point of infinite type with rotation symmetry. The same is shown for “generic” product spaces, as well as for the symmetrized polydisc and the tetrablock. On the other hand, examples of smooth, non-pseudoconvex, Gromov hyperbolic domains in ℂ n