@article{Hadi_Nagy_2021, title={Applications of Affine Systems of Walsh Type to Generate Smooth Basis}, volume={62}, url={https://ijs.uobaghdad.edu.iq/index.php/eijs/article/view/3572}, DOI={10.24996/ijs.2021.62.12.25}, abstractNote={<p>The question on affine Riesz basis of Walsh affine systems is considered. An affine Riesz basis is constructed, generated by a continuous periodic function&nbsp;that belongs to the space on the real line, which has a derivative almost everywhere; in connection with the construction of this example, we note that the functions of the classical Walsh system suffer a discontinuity and their derivatives almost vanish everywhere. A method of regularization (improvement of differential properties) of the generating function of Walsh affine system is proposed, and a criterion for an affine Riesz basis for a regularized generating function that can be represented as a sum of a series in the Rademacher system is obtained.</p>}, number={12}, journal={Iraqi Journal of Science}, author={Hadi, Khaled and Nagy, Saad}, year={2021}, month={Dec.}, pages={4875–4884} }