2009/01/22 by Éric Amar, Eric Amar, Andreas Hartmann +2
Mathematics · #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.CV #msc:30E05 #msc:31A05 #msc:46B15
paper · pdf · doi:10.48550/arxiv.0901.3501
22 pages
arxiv created 2009/01/22 · arxiv updated 2009/12/01
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.