Functions with zero ball means on the quaternionic hyperbolic space
Izvestiya. Mathematics , Tome 66 (2002) no. 5, pp. 875-903.

Voir la notice de l'article provenant de la source Math-Net.Ru

We solve the problem of describing the class of functions with zero integrals over all balls of a common fixed radius on the quaternionic hyperbolic space.
@article{IM2_2002_66_5_a0,
     author = {Vit. V. Volchkov},
     title = {Functions with zero ball means on the quaternionic hyperbolic space},
     journal = {Izvestiya. Mathematics },
     pages = {875--903},
     publisher = {mathdoc},
     volume = {66},
     number = {5},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_5_a0/}
}
TY  - JOUR
AU  - Vit. V. Volchkov
TI  - Functions with zero ball means on the quaternionic hyperbolic space
JO  - Izvestiya. Mathematics 
PY  - 2002
SP  - 875
EP  - 903
VL  - 66
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2002_66_5_a0/
LA  - en
ID  - IM2_2002_66_5_a0
ER  - 
%0 Journal Article
%A Vit. V. Volchkov
%T Functions with zero ball means on the quaternionic hyperbolic space
%J Izvestiya. Mathematics 
%D 2002
%P 875-903
%V 66
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2002_66_5_a0/
%G en
%F IM2_2002_66_5_a0
Vit. V. Volchkov. Functions with zero ball means on the quaternionic hyperbolic space. Izvestiya. Mathematics , Tome 66 (2002) no. 5, pp. 875-903. http://geodesic.mathdoc.fr/item/IM2_2002_66_5_a0/

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

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

[3] Zalcman L., “A bibliographic survey of the Pompeiu problem”, Approximation by solutions of partial differential equations, eds. B. Fuglede et al., Kluwer Acad. Publ., Dordrecht, 1992, 185–194 | MR

[4] Netuka I., Vesely J., “Mean value property and harmonic functions”, Classical and Modern potential Theory and Applications, Kluwer Acad. Publ., Dordrecht, 1994, 359–398 | MR | Zbl

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

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

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

[8] Volchkov V. V., “O mnozhestvakh in'ektivnosti preobrazovaniya Pompeiyu”, Matem. sb., 190:11 (1999), 51–66 | MR | Zbl

[9] Volchkov V. V., “Ekstremalnye zadachi o mnozhestvakh Pompeiyu, II”, Matem. sb., 191:5 (2000), 3–16 | MR | Zbl

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

[11] Volchkov V. V., “O mnozhestvakh in'ektivnosti preobrazovaniya Radona na sferakh”, Izv. RAN. Ser. matem., 63:3 (1999), 63–76 | MR

[12] Volchkov V. V., “Ob odnoi probleme Zaltsmana i ee obobscheniyakh”, Matem. zametki, 53:2 (1993), 30–36 | MR | Zbl

[13] Volchkov V. V., “Okonchatelnyi variant teoremy o srednem v teorii garmonicheskikh funktsii”, Matem. zametki, 59:3 (1996), 351–358 | MR | Zbl

[14] Volchkov V. V., “Teoremy edinstvennosti dlya nekotorykh klassov funktsii s nulevymi sfericheskimi srednimi”, Matem. zametki, 62:1 (1997), 59–65 | MR | Zbl

[15] Volchkov V. V., “Okonchatelnyi variant lokalnoi teoremy o dvukh radiusakh na giperbolicheskikh prostranstvakh”, Izv. RAN. Ser. matem., 65:2 (2001), 3–26 | MR | Zbl

[16] Volchkov V. V., “Teoremy o dvukh radiusakh na prostranstvakh postoyannoi krivizny”, Dokl. RAN, 347:3 (1996), 300–302 | MR | Zbl

[17] Volchkov V. V., “Morera type theorems on the unit disk”, Anal. Math., 20 (1994), 49–63 | DOI | MR | Zbl

[18] Volchkov V. V., “Teoremy o srednem dlya odnogo klassa polinomov”, Sib. matem. zhurn., 35:4 (1994), 737–745 | MR | Zbl

[19] Volchkov V. V., “Problemy tipa Pompeiyu na mnogoobraziyakh”, Dokl. AN Ukrainy, 1993, no. 11, 9–12 | MR

[20] Volchkov Vit. V., “O funktsiyakh s nulevymi sharovymi srednimi na kompleksnykh giperbolicheskikh prostranstvakh”, Matem. zametki, 68:4 (2000), 504–512 | MR | Zbl

[21] Berenstein C. A., Shahshahani M., “Harmonic analysis and Pompeiu problem”, Amer. J. Math., 105 (1983), 1217–1229 | DOI | MR | Zbl

[22] Shahshahani M., Sitaram A., “The Pompeiu problem in exterior domains in Symmetric spaces”, Contemp. Math., 63 (1987), 267–278 | MR

[23] Berenstein C. A., Zalcman L., “Pompeiu's problem on symmetric spaces”, Comment. Math. Helvetici, 55 (1980), 593–621 | DOI | MR | Zbl

[24] Fomenko A. T., Simplekticheskaya geometriya. Metody i prilozheniya, Izd-vo MGU, M., 1988 | MR | Zbl

[25] Rudin U., Teoriya funktsii v edinichnom share iz $C^n$, Mir, M., 1984 | MR | Zbl

[26] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. 1, Nauka, M., 1965

[27] Korenev B. G., Vvedenie v teoriyu besselevykh funktsii, Nauka, M., 1971 | MR | Zbl

[28] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[29] Harchaoui M., “Inversion de la transformation de Pompeiu locale dans les espaces hyperboliques reel et complete (Cas de deux boules)”, J. Anal. Math., 67 (1995), 1–37 | DOI | MR | Zbl

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

[31] Zhelobenko D. P., Shtern A. I., Predstavleniya grupp Li, Nauka, M., 1983 | MR

[32] Volf Dzh., Prostranstva postoyannoi krivizny, Nauka, M., 1982 | MR

[33] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, Nauka, M., 1979 | MR

[34] Shabat B. V., Vvedenie v kompleksnyi analiz, Ch. 2, Nauka, M., 1985 | MR

[35] Vilenkin N. Ya., Spetsialnye funktsii i teoriya predstavlenii grupp, 2-e izd., Nauka, M., 1991 | MR | Zbl