Geodesic
On the Representation of Measurable Functions by Absolutely Convergent Orthogonal Spline Series
Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 73-82

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We show that if $\{f_n(t)\}_{n=-m+2}^{\infty }$ is an orthonormal system in $L^2[0,1]$ consisting of splines of order $m$ with dyadic rational knots and $f(t)$ is an a.e. finite measurable function, then, first, there exists a series with respect to this system that converges absolutely a.e. to this function and, second, for any $\varepsilon >0$ the function $f(t)$ can be changed on a set of measure less than $\varepsilon $ so that the corrected function has a uniformly absolutely convergent Fourier series with respect to this system.
Keywords: spline of order $m$, absolutely convergent series, representation of functions, correction of functions. 
G. G. Gevorkyan. On the Representation of Measurable Functions by Absolutely Convergent Orthogonal Spline Series. Informatics and Automation, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 73-82. http://geodesic.mathdoc.fr/item/TRSPY_2022_319_a5/
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