Displaying similar documents to “Local holomorphic extendability and non-extendability of C R -functions on smooth boundaries”

On the complex and convex geometry of Ol'shanskii semigroups

Karl-Hermann Neeb (1998)

Annales de l'institut Fourier

Similarity:

To a pair of a Lie group G and an open elliptic convex cone W in its Lie algebra one associates a complex semigroup S = G Exp ( i W ) which permits an action of G × G by biholomorphic mappings. In the case where W is a vector space S is a complex reductive group. In this paper we show that such semigroups are always Stein manifolds, that a biinvariant domain D ⊆ S is Stein is and only if it is of the form G Exp ( D h ) , with D h ⊆ i W convex, that each holomorphic function on D extends to the smallest biinvariant Stein domain...

Maximum modulus sets and reflection sets

Alexander Nagel, Jean-Pierre Rosay (1991)

Annales de l'institut Fourier

Similarity:

We study sets in the boundary of a domain in C n , on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to , which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.