• Corpus ID: 118618112

# Weak and strong regularity, compactness, and approximation of polynomials

@article{Schrijver2012WeakAS,
title={Weak and strong regularity, compactness, and approximation of polynomials},
author={Alexander Schrijver},
journal={arXiv: Combinatorics},
year={2012}
}
• A. Schrijver
• Published 15 November 2012
• Mathematics
• arXiv: Combinatorics
Let $X$ be an inner product space, let $G$ be a group of orthogonal transformations of $X$, and let $R$ be a bounded $G$-stable subset of $X$. We define very weak and very strong regularity for such pairs $(R,G)$ (in the sense of Szemer\'edi's regularity lemma), and prove that these two properties are equivalent. Moreover, these properties are equivalent to the compactness of the space $(B(H),d_R)/G$. Here $H$ is the completion of $X$ (a Hilbert space), $B(H)$ is the unit ball in $H$, $d_R$ is…

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