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Displaying 521 –
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The well known theorem of Rogosinski asserts that if the modulus of the sum of a power series is less than 1 in the open unit disk: , |z| < 1, then all its partial sums are less than 1 in the disk of radius 1/2:
, |z| < 1/2,
and this radius is sharp. We present a generalization of this theorem to holomorphic mappings of the open unit ball into an arbitrary convex domain. Other multidimensional analogs of Rogosinski’s theorem as well as some applications to dynamical systems are considered....
We study the regularity of the induced foliation of a Levi-flat hypersurface in Cn, showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question.
We give several characterizations of the symmetrized n-disc Gₙ which generalize to the case n ≥ 3 the characterizations of the symmetrized bidisc that were used in order to solve the two-point spectral Nevanlinna-Pick problem in ℳ ₂(ℂ). Using these characterizations of the symmetrized n-disc, which give necessary and sufficient conditions for an element to belong to Gₙ, we obtain necessary conditions of interpolation for the general spectral Nevanlinna-Pick problem. They also allow us to give a...
Si esamina la successione spettrale per la -coomologia dello spazio totale di un fibrato olomorfo nel caso in cui le fibre siano varietà di Stein.
We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.
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