Almost-Orthogonality of Restricted Haar-Functions

Julian Weigt

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arXiv · 1807.10809

Almost-Orthogonality of Restricted Haar-Functions

Julian Weigt

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Abstract

We consider the Haar functions $h_I$ on dyadic intervals. We show that if $p>\frac23$ and $E\subset[0,1]$ then the set of all functions $\|h_I1_E\|_2^{-1}h_I1_E$ with $|I\cap E|\geq p|I|$ is a Riesz sequence. For $p\leq\frac23$ we provide a counterexample.

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Julian Weigt. 2018-07-27. Almost-Orthogonality of Restricted Haar-Functions. https://arxiv.org/abs/1807.10809

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