2011/10/08 by Frédéric Gaunard, Frederic Gaunard, Gaunard, Frederic
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Stability and Controllability of Differential Equations #math.CV
paper · pdf · doi:10.48550/arxiv.1110.1714
18 pages
arxiv created 2011/10/08 · openalex publication_date 2011/10/08 · arxiv updated 2011/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known from a result by Shapiro-Shields that in the Hardy spaces, a sequence of reproducing kernels is uniformly minimal if and only if it is an unconditional basis in its span. This property which can be reformulated in terms of interpolation and so-called weak interpolation is not true in Paley-Wiener spaces in general. Here we show that the Carleson condition on a sequence Λ together with minimality in Paley-Wiener spaces PWτp of the associated sequence of reproducing kernels implies the interpolation property of Λ in PWτ+εp, for every ε>0. With the same technics, using a result of McPhail, we prove a similary result about minimlity and weighted interpolation in PWτ+εp.. We apply the results to control theory, establishing that, under some hypotheses, a certain weak type of controllability in time τ>0 implies exact controllability in time τ+ε, for every ε>0.