Interpolation problems for functions with zero integrals over balls of fixed radius
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 20-23
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Let $V_r(\mathbb{R}^n)$, $n\ge2$, be the set of functions $f\in L_{\operatorname{loc}}(\mathbb{R}^n)$ with zero integrals over all balls in $\mathbb{R}^n$ of radius $r$. Various interpolation problems for the class $V_r(\mathbb{R}^n)$ are studied. In the case when the set of interpolation nodes is finite, the multiple interpolation problem is solved under general assumptions. For problems with an infinite set of nodes, sufficient solvability conditions are founded. Additionally, we construct a new example of a subset in $\mathbb{R}^n$ for which some nontrivial real analytic function of the class $V_r(\mathbb{R}^n)$ vanishes.
Keywords:
interpolation problems, spherical means, mean periodicity.
@article{DANMA_2020_490_a4,
author = {V. V. Volchkov and Vit. V. Volchkov},
title = {Interpolation problems for functions with zero integrals over balls of fixed radius},
journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
pages = {20--23},
publisher = {mathdoc},
volume = {490},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DANMA_2020_490_a4/}
}
TY - JOUR AU - V. V. Volchkov AU - Vit. V. Volchkov TI - Interpolation problems for functions with zero integrals over balls of fixed radius JO - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ PY - 2020 SP - 20 EP - 23 VL - 490 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DANMA_2020_490_a4/ LA - ru ID - DANMA_2020_490_a4 ER -
%0 Journal Article %A V. V. Volchkov %A Vit. V. Volchkov %T Interpolation problems for functions with zero integrals over balls of fixed radius %J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ %D 2020 %P 20-23 %V 490 %I mathdoc %U http://geodesic.mathdoc.fr/item/DANMA_2020_490_a4/ %G ru %F DANMA_2020_490_a4
V. V. Volchkov; Vit. V. Volchkov. Interpolation problems for functions with zero integrals over balls of fixed radius. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 20-23. http://geodesic.mathdoc.fr/item/DANMA_2020_490_a4/