Displaying similar documents to “Approximation in ℂ N .”

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.

On the multivariate transfinite diameter

Thomas Bloom, Jean-Paul Calvi (1999)

Annales Polonici Mathematici

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We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.

On a class of ∂ ¯ -equations without solutions

Telemachos Hatziafratis (1998)

Commentationes Mathematicae Universitatis Carolinae

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In this note we construct ∂ ¯ -equations (inhomogeneous Cauchy-Riemann equations) without solutions. The construction involves Bochner-Martinelli type kernels and differentiation with respect to certain parameters in appropriate directions.

An approximation theorem related to good compact sets in the sense of Martineau

Jean-Pierre Rosay, Edgar Lee Stout (2000)

Annales de l'institut Fourier

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This note contains an approximation theorem that implies that every compact subset of ℂ n is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.

A new division formula for complete intersections

Mikael Passare (1991)

Annales Polonici Mathematici

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We provide a new division formula for holomorphic mappings. It is given in terms of residue currents and has the advantage of being more explicit and simpler to prove than the previously known formulas.

On D*-extension property of the Hartogs domains.

Do Duc Thai, Pascal J. Thomas (2001)

Publicacions Matemàtiques

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A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is...