English

Parseval frames of piecewise constant functions

Functional Analysis 2019-01-10 v2

Abstract

We present a way to construct Parseval frames of piecewise constant functions for L2[0,1]L^2[0,1]. The construction is similar to the generalized Walsh bases. It is based on iteration of operators that satisfy a Cuntz-type relation, but without the isometry property. We also show how the Parseval frame can be dilated to an orthonormal basis and the operators can be dilated to true Cuntz isometries.

Keywords

Cite

@article{arxiv.1804.03577,
  title  = {Parseval frames of piecewise constant functions},
  author = {Dorin Ervin Dutkay and Rajitha Ranasinghe},
  journal= {arXiv preprint arXiv:1804.03577},
  year   = {2019}
}
R2 v1 2026-06-23T01:19:28.473Z