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Almost-orthogonality of restricted Haar functions


Author: Julian Weigt
Journal: Proc. Amer. Math. Soc. 148 (2020), 601-609
MSC (2010): Primary 42C10
DOI: https://doi.org/10.1090/proc/14752
Published electronically: October 18, 2019
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Abstract: We consider the Haar functions $ h_I$ on dyadic intervals. We show that if $ p>\frac 23$ and $ E\subset [0,1]$, then the set of all functions $ \Vert h_I1_E\Vert _2^{-1}h_I1_E$ with $ \vert I\cap E\vert\geq p\vert I\vert$ is a Riesz sequence. For $ p\leq \frac 23$ we provide a counterexample.


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Additional Information

Julian Weigt
Affiliation: Department of Mathematics and Systems Analysis, Aalto University, FI-00076 Aalto, Finland

DOI: https://doi.org/10.1090/proc/14752
Received by editor(s): July 27, 2018
Received by editor(s) in revised form: February 20, 2019
Published electronically: October 18, 2019
Communicated by: Svitlana Mayboroda
Article copyright: © Copyright 2019 American Mathematical Society