Parseval frames of piecewise constant functions

2018/04/10 by Dutkay, Dorin Ervin, Ranasinghe, Rajitha
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1804.03577

Abstract

We present a way to construct Parseval frames of piecewise constant functions for L²[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.

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