Reproducing Kernels for the Irreducible Components of Polynomial Spaces on Unions of Grassmannians
Reproducing Kernels for the Irreducible Components of Polynomial Spaces on Unions of Grassmannians
The decomposition of polynomial spaces on unions of Grassmannians $${\mathcal {G}}_{{k_1},d}\cup \ldots \cup \mathcal G_{{k_r},d}$$ into irreducible orthogonally invariant subspaces and their reproducing kernels are investigated. We also generalize the concepts of cubature points and t-designs from single Grassmannians to unions. We derive their characterization as minimizers of a suitable …