Displaying similar documents to “The Lindelöf principle in ℂn”

Holomorphic functions of fast growth on submanifolds of the domain

Piotr Jakóbczak (1998)

Annales Polonici Mathematici

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We construct a function f holomorphic in a balanced domain D in ℂ N such that for every positive-dimensional subspace Π of ℂ N , and for every p with 1 ≤ p < ∞, f | Π ∩ D is not L p -integrable on Π ∩ D.

The ends of discs

Josip Globevnik, Edgar Lee Stout (1986)

Bulletin de la Société Mathématique de France

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Extending holomorphic maps in infinite dimensions

Bui Dac Tac (1991)

Annales Polonici Mathematici

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Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results...

Maximum modulus sets and reflection sets

Alexander Nagel, Jean-Pierre Rosay (1991)

Annales de l'institut Fourier

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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.