# On Generalized Walsh Bases

@article{Dutkay2018OnGW, title={On Generalized Walsh Bases}, author={Dorin Ervin Dutkay and Gabriel Picioroaga and Sergei Silvestrov}, journal={Acta Applicandae Mathematicae}, year={2018}, pages={1-18} }

This paper continues the study of orthonormal bases (ONB) of L2[0,1]$L^{2}[0,1]$ introduced in Dutkay et al. (J. Math. Anal. Appl. 409(2):1128–1139, 2014) by means of Cuntz algebra ON$\mathcal{O}_{N}$ representations on L2[0,1]$L^{2}[0,1]$. For N=2$N=2$, one obtains the classic Walsh system. We show that the ONB property holds precisely because the ON$\mathcal{O}_{N}$ representations are irreducible. We prove an uncertainty principle related to these bases. As an application to discrete signal… Expand

#### 3 Citations

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