Geodesic
Extremal problems on Pompeiu sets. II
Sbornik. Mathematics, Tome 191 (2000) no. 5, pp. 619-632 Cet article a éte moissonné depuis la source Math-Net.Ru

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A solution of the local Pompeiu problem is obtained for functions with vanishing integrals over parallelepipeds lying in a fixed ball. 
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V. V. Volchkov. Extremal problems on Pompeiu sets. II. Sbornik. Mathematics, Tome 191 (2000) no. 5, pp. 619-632. http://geodesic.mathdoc.fr/item/SM_2000_191_5_a0/

[1] Zalcman L., “A bibliographic survey of the Pompeiu problem”, Approximation by solutions of partial differential equations, Proc. NATO Adv. Res. Workshop (Hanstholm/Den., 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 365, 1992, 185–194 | MR | Zbl

[2] Berenstein K. A., Struppa D., “Kompleksnyi analiz i uravneniya v svertkakh”, Itogi nauki i tekhn. Sovr. probl. matem. Fundam. napr., 54, VINITI, M., 1989, 5–111 | MR

[3] Volchkov V. V., “Novye teoremy o srednem dlya reshenii uravneniya Gelmgoltsa”, Matem. sb., 184:7 (1993), 71–78 | MR | Zbl

[4] Garofalo N., Segala F., “Univalent functions and the Pompeiu problem”, Trans. Amer. Math. Soc., 346:1 (1994), 137–146 | DOI | MR | Zbl

[5] Ullrich D. C., “More on the Pompeiu problem”, Amer. Math. Monthly, 101 (1994), 165–168 | DOI | MR | Zbl

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

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

[8] Berenstein C. A., Gay R.,Yger A., “The three squares theorem, a local version”, Analysis and Partial Differential Equations, ed. C. Sadosky, Marcel Deccer, New York, 1990, 35–50 | MR

[9] Volchkov V. V., “Ekstremalnye zadachi o mnozhestvakh Pompeiyu”, Matem. sb., 189:7 (1998), 3–22 | MR | Zbl

[10] Volchkov V. V., “Ekstremalnye varianty problemy Pompeiyu”, Matem. zametki, 59:5 (1996), 671–680 | MR | Zbl

[11] Volchkov V. V., “Ob odnoi ekstremalnoi zadache, svyazannoi s teoremoi Morery”, Matem. zametki, 60:6 (1996), 804–809 | MR | Zbl

[12] Volchkov V. V., “Okonchatelnyi variant lokalnoi teoremy o dvukh radiusakh”, Matem. sb., 186:6 (1995), 15–34 | MR | Zbl

[13] Volchkov V. V., “Reshenie problemy nositelya dlya nekotorykh klassov funktsii”, Matem. sb., 188:9 (1997), 13–30 | MR | Zbl

[14] Volchkov V. V., “Novye teoremy o dvukh radiusakh v teorii garmonicheskikh funktsii”, Izv. RAN. Ser. matem., 58:1 (1994), 182–194 | Zbl

[15] Volchkov V. V., “Approksimatsiya funktsii na ogranichennykh oblastyakh v $\mathbb R^n$ lineinymi kombinatsiyami sdvigov”, Dokl. AN, 334:5 (1994), 560–561 | MR | Zbl

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

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

[18] Khelgason S., Gruppy i geometricheskii analiz, Mir, M., 1987 | MR