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

Martin Ehler; Manuel Gräf

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arXiv · 1411.5865

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

Martin Ehler·Manuel Gräf

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Abstract

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 energy potential to enable $t$-design constructions by numerical optimization. We also present new analytic families of $t$-designs for $t=1,2,3$.

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Martin Ehler, Manuel Gräf. 2014-11-21. Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians. https://arxiv.org/abs/1411.5865

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