Reproducing kernels for the irreducible components of polynomial spaces\n on unions of Grassmannians

2014/11/21 by Martin Ehler, Ehler, Martin, Manuel Gräf +1 · 1 citation
Decision Sciences · Engineering · Mathematics · #Optimal Experimental Design Methods #graph theory and CDMA systems #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1411.5865

Abstract

The decomposition of polynomial spaces on unions of Grassmannians mathcal\nG_k₁,d\∪\…\∪ mathcal G_k_r,d into irreducible orthogonally\ninvariant subspaces and their reproducing kernels are investigated. We also\ngeneralize the concepts of cubature points and t-designs from single\nGrassmannians to unions. We derive their characterization as minimizers of a\nsuitable energy potential to enable t-design constructions by numerical\noptimization. We also present new analytic families of t-designs for\nt=1,2,3.\n

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