Uniform minimality, unconditionality and interpolation in backward shift invariant spaces

Eric Amar (1) , Andreas Hartmann (1)

1 IMB - Institut de Mathématiques de Bordeaux

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 other scales of spaces), changing the size of the space seems %in this context necessary to deduce unconditionality or interpolation from uniform minimality. Such a change can take two directions: lowering the power of integration, or ''increasing'' the defining inner function (e.g.\ increasing the type in the case of Paley-Wiener space). Khinchin's inequalities play a substantial rôle in the proofs of our main results.

Mots clés: Uniform minimality; unconditional bases; model spaces; Paley-Wiener spaces; interpolation; one-component inner functions

Domaines: Variables complexes [math.CV]

Eric Amar, Andreas Hartmann. Uniform minimality, unconditionality and interpolation in backward shift invariant spaces. Annales de l'Institut Fourier, 2010, 60 (1), pp.1879-1903. ⟨hal-00355323⟩