Description
Last week Mita Ramabulana explained what the Arestov-Babenko method can give in establishing linear programming strong duality for general Delsarte-type extremal problems. The method worked in quite some generality, could even handle two-sided sign restrictions, and the method lends itself to generalizations to homogeneous spaces and compact Gelfand pairs, too. However, compactness had to be assumed in all cases.
In the Delsarte case of only one-sided sign restrictions, recent results of Cohn-de Laat-Salmon and Kolountzakis-Lev-Matolcsi establish the strong duality in R^d, with essential use of the Euclidean structure. On the set of non-positivity Cohn at al. are quite general, however, they find a strong dual only in the space of tempered distributions. With a mild topological condition on the restriction set, Kolountzakis at al. obtains better described duals already in the space of translation bounded measures.
We also recall a functional analytic idea of Virosztek, which worked well for Z^d and in fact mutatis mutandis also for discrete groups.
Joint work with Elena E. Berdysheva, Bálint Farkas, Marcell Gaál and Mita D. Ramabulana.