Geodesic
Recovery of Functions on $p$-Adic Groups
Matematičeskie zametki, Tome 112 (2022) no. 6, pp. 867-878

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A general definition of recovering set for the class of integrable functions is introduced. For every Zygmund class $\Lambda$ on the $p$-adic group, the existence of such sets is proved, and procedures for the complete recovery of a function $f \in \Lambda$ and its Fourier coefficients in the Vilenkin–Chrestenson system from the values of $f$ on one of these sets are given. We also study the more general case in which $p$-adic measures or general Vilenkin–Chrestenson series rather than $L^1$-functions are considered.
Mots-clés : $p$-adic group, Fourier coefficient
Keywords: Vilenkin–Chrestenson function, $p$-ary tree, quasi-measure. 
@article{MZM_2022_112_6_a6,
     author = {M. G. Plotnikov and V. S. Astashonok},
     title = {Recovery of {Functions} on $p${-Adic} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {867--878},
     publisher = {mathdoc},
     volume = {112},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a6/}
}
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M. G. Plotnikov; V. S. Astashonok. Recovery of Functions on $p$-Adic Groups. Matematičeskie zametki, Tome 112 (2022) no. 6, pp. 867-878. http://geodesic.mathdoc.fr/item/MZM_2022_112_6_a6/