Geodesic
Injectivity sets of the Pompeiu transform
Sbornik. Mathematics, Tome 190 (1999) no. 11, pp. 1607-1622 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of the description of the injectivity sets of the Pompeiu transform $\mathscr P_\varphi$ is solved for a broad class of distributions $\varphi$ with support on the unit sphere. 
@article{SM_1999_190_11_a2,
     author = {V. V. Volchkov},
     title = {Injectivity sets of the {Pompeiu} transform},
     journal = {Sbornik. Mathematics},
     pages = {1607--1622},
     year = {1999},
     volume = {190},
     number = {11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_11_a2/}
}
TY  - JOUR
AU  - V. V. Volchkov
TI  - Injectivity sets of the Pompeiu transform
JO  - Sbornik. Mathematics
PY  - 1999
SP  - 1607
EP  - 1622
VL  - 190
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/SM_1999_190_11_a2/
LA  - en
ID  - SM_1999_190_11_a2
ER  - 
%0 Journal Article
%A V. V. Volchkov
%T Injectivity sets of the Pompeiu transform
%J Sbornik. Mathematics
%D 1999
%P 1607-1622
%V 190
%N 11
%U http://geodesic.mathdoc.fr/item/SM_1999_190_11_a2/
%G en
%F SM_1999_190_11_a2
V. V. Volchkov. Injectivity sets of the Pompeiu transform. Sbornik. Mathematics, Tome 190 (1999) no. 11, pp. 1607-1622. http://geodesic.mathdoc.fr/item/SM_1999_190_11_a2/

[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. napr., 54, VINITI, M., 1989, 5–111 | MR

[3] 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 ASI Ser., Ser. C, 365, 1992, 185–194 | MR | Zbl

[4] Rawat R., Sitaram A., “The injectivity of the Pompeiu transform and $L^p$-analogues of the Wiener–Tauberian theorem”, Israel J. Math., 91 (1995), 307–316 | DOI | MR | Zbl

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

[6] Quinto E. T., “Pompeiu transforms on geodesic spheres in real analytic manifolds”, Israel J. Math., 84 (1993), 353–363 | DOI | MR | Zbl

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

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

[9] Volchkov V. V., “Okonchatelnyi variant lokalnoi teoremy o dvukh radiusakh”, Matem. sb., 186:6 (1995), 15–34 | 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., “Reshenie problemy nositelya dlya nekotorykh klassov funktsii”, Matem. sb., 188:9 (1997), 13–30 | MR | Zbl

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

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

[14] Berenstein C. A., Gay R., Yger A., “Inversion of the local Pompeiu transform”, J. Anal. Math., 54 (1990), 259–287 | DOI | MR | Zbl

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

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

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

[18] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1976 | MR

[19] Khua Lo-Ken, Garmonicheskii analiz funktsii mnogikh kompleksnykh peremennykh v klassicheskikh oblastyakh, IL, M., 1959

[20] Tolstov G. P., Ryady Fure, Nauka, M., 1980 | MR | Zbl

[21] Shidlovskii A. B., Transtsendentnye chisla, Nauka, M., 1987 | MR

[22] Khermander L., Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, M., 1965 | MR

[23] Khavin V. P., “Metody i struktura kommutativnogo garmonicheskogo analiza”, Itogi nauki i tekhn. Sovr. probl. matem. Fundam. napr., 15, VINITI, M., 1986, 6–134

[24] Palamodov V. P., “Obobschennye funktsii i garmonicheskii analiz”, Itogi nauki i tekhn. Sovr. probl. matem. Fundam. napr., 72, VINITI, M., 1991, 5–134 | MR