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On linear extension for interpolating sequences

Eric Amar — 2008

Studia Mathematica

Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces H p ( σ ) and the H p ( σ ) interpolating sequences S in the p-spectrum p of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is H s ( σ ) -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in H ( ) then S is H p ( ) -interpolating with a linear...

On the Toëplitz corona problem.

Eric Amar — 2003

Publicacions Matemàtiques

The aim of this note is to characterize the vectors g = (g, . . . ,g) of bounded holomorphic functions in the unit ball or in the unit polydisk of C such that the Corona is true for them in terms of the H Corona for measures on the boundary.

Interpolating sequences, Carleson measures and Wirtinger inequality

Eric Amar — 2008

Annales Polonici Mathematici

Let S be a sequence of points in the unit ball of ℂⁿ which is separated for the hyperbolic distance and contained in the zero set of a Nevanlinna function. We prove that the associated measure μ S : = a S ( 1 - | a | ² ) δ a is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of such that any δ -separated sequence S has its associated measure μ S bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of . As an easy consequence, we prove that if S is a dual bounded sequence...

Uniform minimality, unconditionality and interpolation in backward shift invariant subspaces

Eric AmarAndreas Hartmann — 2010

Annales de l’institut Fourier

We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of standard Hardy spaces (and of other scales of spaces), changing the size of the space seems necessary to deduce unconditionality...

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