Geodesic
On some properties of functions characterized by zero integrals
Matematičeskoe obrazovanie, no. 4 (2021), pp. 38-48 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article introduces the reader to studying a class of functions that have zero integrals over all squares of a fixed size, lying in a given circle. A criterion for the total differential in a strengthened form is given, as well as generalizations of other classical results related to zero integrals are considered. 
@article{MO_2021_4_a6,
     author = {V. V. Volchkov and Vit. V. Volchkov and N. P. Volchkova},
     title = {On some properties of functions characterized by zero integrals},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {38--48},
     year = {2021},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2021_4_a6/}
}
TY  - JOUR
AU  - V. V. Volchkov
AU  - Vit. V. Volchkov
AU  - N. P. Volchkova
TI  - On some properties of functions characterized by zero integrals
JO  - Matematičeskoe obrazovanie
PY  - 2021
SP  - 38
EP  - 48
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MO_2021_4_a6/
LA  - ru
ID  - MO_2021_4_a6
ER  - 
%0 Journal Article
%A V. V. Volchkov
%A Vit. V. Volchkov
%A N. P. Volchkova
%T On some properties of functions characterized by zero integrals
%J Matematičeskoe obrazovanie
%D 2021
%P 38-48
%N 4
%U http://geodesic.mathdoc.fr/item/MO_2021_4_a6/
%G ru
%F MO_2021_4_a6
V. V. Volchkov; Vit. V. Volchkov; N. P. Volchkova. On some properties of functions characterized by zero integrals. Matematičeskoe obrazovanie, no. 4 (2021), pp. 38-48. http://geodesic.mathdoc.fr/item/MO_2021_4_a6/

[1] I. M. Gelfand, S. G. Gindikin, M. I. Graev, Izbrannye zadachi integralnoi geometrii, Dobrosvet, M., 2000, 208 pp. | MR

[2] F. Ion, Ploskie volny i sfericheskie srednie v primenenii k differentsialnym uravneniyam s chastnymi proizvodnymi, IL, M., 1958, 158 pp.

[3] S. Khelgason, Preobrazovanie Radona, Mir, M., 1983, 152 pp. | MR

[4] V. A. Zorich, Matematicheskii analiz II, Nauka, M., 1984, 640 pp. | MR

[5] V. S. Vladimirov, Uravneniya matematicheskoi fiziki, Nauka, M., 1981, 512 pp. | MR

[6] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989, 624 pp. | MR

[7] H. Cramér, H. Wold, “Some theorems on distribution functions”, J. London Math. Soc., 11:2 (1936), 290–294 | DOI | MR

[8] B. Gelbaum, Dzh. Olmsted, Kontrprimery v analize, Mir, M., 1967, 252 pp. | MR