Geodesic
Uniqueness theorems for some classes of functions with zero spherical means
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 59-65.

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

We study various classes of functions that have zero integrals over all spheres of given radius. For these functions, we obtain a description in the form of a series in special functions; the problem of the existence of a nonzero function of prescribed growth with this property is completely solved. 
@article{MZM_1997_62_1_a5,
     author = {V. V. Volchkov},
     title = {Uniqueness theorems for some classes of functions with zero spherical means},
     journal = {Matemati\v{c}eskie zametki},
     pages = {59--65},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a5/}
}
TY  - JOUR
AU  - V. V. Volchkov
TI  - Uniqueness theorems for some classes of functions with zero spherical means
JO  - Matematičeskie zametki
PY  - 1997
SP  - 59
EP  - 65
VL  - 62
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a5/
LA  - ru
ID  - MZM_1997_62_1_a5
ER  - 
%0 Journal Article
%A V. V. Volchkov
%T Uniqueness theorems for some classes of functions with zero spherical means
%J Matematičeskie zametki
%D 1997
%P 59-65
%V 62
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a5/
%G ru
%F MZM_1997_62_1_a5
V. V. Volchkov. Uniqueness theorems for some classes of functions with zero spherical means. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 59-65. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a5/

[1] Smith J. D., “Harmonic analysis of scalar and vector fields in $\mathbb R^n$”, Proc. Cambridge Philos. Soc., 72 (1972), 403–416 | DOI | MR | Zbl

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

[3] Thangavelu S., Spherical means and CR functions on the Heisenberg group, Preprint, Cornell Univ. (Ithaca, NY 14850), 1984

[4] Zalcman L., “Offbeat integral geometry”, Amer. Math. Monthly, 37:161–175 (1980) | MR

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

[6] Volchkov V. V., “Novye teoremy o dvukh radiusakh v teorii garmonicheskikh funktsii”, Izv. RAN. Ser. matem., 58:1 (1994), 41–49 | MR

[7] Tolstov G. P., Ryady Fure, 3-e izd., Nauka, M., 1980 | Zbl

[8] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964