TY - JOUR
AU - Hadi, Khaled
AU - Nagy, Saad
PY - 2021/12/30
Y2 - 2022/09/28
TI - Applications of Affine Systems of Walsh Type to Generate Smooth Basis
JF - Iraqi Journal of Science
JA - eijs
VL - 62
IS - 12
SE - Mathematics
DO - 10.24996/ijs.2021.62.12.25
UR - https://ijs.uobaghdad.edu.iq/index.php/eijs/article/view/3572
SP - 4875-4884
AB - <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 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>
ER -