Geodesic
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. 
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     title = {Interpolation problems for functions with zero integrals over balls of fixed radius},
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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/

[1] Zalcman L., Approximation by Solutions of Partial Differential Equations, 1992, 185–194 | DOI | Zbl

[2] Volchkov V.V., Volchkov Vit.V., Offbeat Integral Geometry on Symmetric Spaces, Birkhäuser, Basel, 2013, 592 pp. | MR | Zbl

[3] Berenstein K.A., Struppa D., Itogi nauki i tekhn. Sovrem. probl. matem. Fundament. napravleniya, 54, VINITI, M., 1989, 5–111

[4] Zalcman L., Contemp. Math., 278, 2001, 69–74 | DOI | MR | Zbl

[5] Volchkov V.V., Integral geometry and convolution equations, Kluwer, Dordrecht, 2003, 454 pp. | MR | Zbl

[6] Volchkov V.V., Volchkov Vit.V., Harmonic analysis of mean periodic functions on symmetric spaces and the Heisenberg group, Springer, L., 2009, 671 pp. | MR | Zbl

[7] Ion F., Ploskie volny i sfericheskie srednie v primenenii k differentsialnym uravneniyam s chastnymi proizvodnymi, IL, M., 1958, 158 pp.

[8] Smith J.D., Proc. Cambridge Philos. Soc, 72 (1972), 403–416 | DOI | MR | Zbl

[9] Rawat R., Sitaram A., Israel J. Math., 91 (1995), 307–316 | DOI | MR | Zbl

[10] Thangavelu S., J. Anal. Math., 63 (1994), 225–286 | DOI | MR

[11] Evgrafov M.A., Asimptoticheskie otsenki i tselye funktsii, Fizmatgiz, M., 1962, 320 pp. | MR

[12] Schneider R., J. Math. Anal. Appl., 26 (1969), 381–384 | DOI | MR | Zbl

[13] Volchkov V.V., Matem. sbornik, 188:9 (1997), 13–30 | DOI | MR | Zbl

[14] Volchkov Vit.V., Volchkova N.P., Sib. mat. zhurn., 58:3 (2017), 543–552 | MR | Zbl

[15] Berkani M., El Harchaoui, Gay R., Complex Variables, 43 (2000), 29–57 | MR | Zbl