Geodesic
A Sobolev Orthogonal System of Functions Generated by a Walsh System
Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 545-552

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Properties of functions from the Sobolev orthogonal system $\mathfrak W_r$ generated by the Walsh system are studied. In particular, recurrence relations for functions from $\mathfrak W_1$ are obtained. The uniform convergence of Fourier series in the system $\mathfrak W_r$ to functions $f$ from the Sobolev spaces $W^r_{L^p}$, $p\ge 1$, $r=1,2,\dots$ is proved.
Keywords: Sobolev orthogonality, Walsh system, recurrence relation.
Mots-clés : uniform convergence 
@article{MZM_2019_105_4_a5,
     author = {M. G. Magomed-Kasumov},
     title = {A {Sobolev} {Orthogonal} {System} of {Functions} {Generated} by a {Walsh} {System}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {545--552},
     publisher = {mathdoc},
     volume = {105},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a5/}
}
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M. G. Magomed-Kasumov. A Sobolev Orthogonal System of Functions Generated by a Walsh System. Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 545-552. http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a5/