English

Almost-Orthogonality of Restricted Haar-Functions

Functional Analysis 2019-12-24 v2

Abstract

We consider the Haar functions hIh_I on dyadic intervals. We show that if p>23p>\frac23 and E[0,1]E\subset[0,1] then the set of all functions hI1E21hI1E\|h_I1_E\|_2^{-1}h_I1_E with IEpI|I\cap E|\geq p|I| is a Riesz sequence. For p23p\leq\frac23 we provide a counterexample.

Keywords

Cite

@article{arxiv.1807.10809,
  title  = {Almost-Orthogonality of Restricted Haar-Functions},
  author = {Julian Weigt},
  journal= {arXiv preprint arXiv:1807.10809},
  year   = {2019}
}