Geodesic
Extremal cases of the Pompeiu problem
Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 671-680.

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The Pompeiu problem is studied for functions defined on a ball $B\subset\mathbb R^n$ and having zero integrals over all sets congruent to a given compact set $K\subset B$. The problem of finding the least radius $r=r(K)$ of $B$ for which $K$ is a Pompeiu set is considered. The solution is obtained for the cases in which $K$ is a cube or a hemisphere. 
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V. V. Volchkov. Extremal cases of the Pompeiu problem. Matematičeskie zametki, Tome 59 (1996) no. 5, pp. 671-680. http://geodesic.mathdoc.fr/item/MZM_1996_59_5_a2/

[1] Zalcman L., A bibliographical survey of the Pompeiu problem. Approximation by solution of partial differential equations, quadrature formula and related topics, eds. M. Goldstein, W. Haussman, Kluwer Academic Publishers, 1992

[2] Berenstein C. A., Gay R., “Le probleme de Pompeiu locale”, J. Analyse Math., 52 (1989), 133–166 | DOI | MR | Zbl

[3] Berenstein C. A., Gay R., “A local version of the two-circles theorem”, Israel J. Math., 55 (1986), 267–288 | DOI | MR | Zbl

[4] Volchkov V. V., “O funktsiyakh s nulevymi integralami po kubam”, Ukr. matem. zh., 43:6 (1991), 859–863 | MR | Zbl

[5] Szabo G., “On fuctions having the same integral on congruent semidiscs”, Ann. Univ. Sci. Budapest. Lec. Computator, 3 (1982), 3–9 | Zbl

[6] Vilenkin N. Ya., Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1991 | Zbl

[7] Volchkov V. V., Teoremy o vzveshennykh sfericheskikh srednikh dlya nekotorykh polinomov, Dep. UkrINTEI. No. 345–Uk93, DonGU, Donetsk, 1993

[8] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl

[9] Khelgason S., Gruppy i geometricheskii analiz, Mir, M., 1987

[10] Volchkov V. V., “Teoremy edinstvennosti dlya kratnykh lakunarnykh trigonometricheskikh ryadov”, Matem. zametki, 51:6 (1992), 27–31 | MR | Zbl

[11] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956