Geodesic
The solution of the generalized convolution equation
Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 317-338.

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

The following equation is considered: $$ \sum_{k=0}^p\int_a^b f^{(k)}(x+t)\,d\sigma_k(t)=0, $$ where the functions $\sigma_k(t)$ are of bounded variation on $[a,b]$, the function $\sigma_p(t)$ having jumps at the end points. A series of elementary solutions is associated with the solution by a certain rule (RZhMat., 1966, 4B106). The convergence of this series is investigated. The results of Sedletskii (RZhMat., 1971, 6B114) for the case $p=0$ are used. Bibliography: 5 titles. 
@article{IM2_1980_14_2_a5,
     author = {A. F. Leont'ev},
     title = {The solution of the generalized convolution equation},
     journal = {Izvestiya. Mathematics },
     pages = {317--338},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a5/}
}
TY  - JOUR
AU  - A. F. Leont'ev
TI  - The solution of the generalized convolution equation
JO  - Izvestiya. Mathematics 
PY  - 1980
SP  - 317
EP  - 338
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a5/
LA  - en
ID  - IM2_1980_14_2_a5
ER  - 
%0 Journal Article
%A A. F. Leont'ev
%T The solution of the generalized convolution equation
%J Izvestiya. Mathematics 
%D 1980
%P 317-338
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a5/
%G en
%F IM2_1980_14_2_a5
A. F. Leont'ev. The solution of the generalized convolution equation. Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 317-338. http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a5/

[1] Leontev A. F., “O preobrazovanii odnogo funktsionalnogo uravneniya k bolee prostomu vidu”, Matem. sb., 67(109):4 (1965), 541–560 | MR

[2] Sedletskii A. M., “O funktsiyakh, periodicheskikh v srednem”, Izv. AN SSSR. Ser. matem., 34 (1970), 1391–1415 | MR

[3] Sedletskii A. M., “Periodicheskoe v srednem prodolzhenie nepreryvnykh funktsii s sokhraneniem gladkosti”, Dokl. AN SSSR, 212:2 (1973), 302–304

[4] Sedletskii A. M., “O polnote sistemy eksponent v prostranstvakh differentsiruemykh funktsii”, Tr. Mosk. energ. in-ta (tematich. sb., voprosy teorii signalov v radiotekhnicheskikh sistemakh), 334, 1977, 98–103

[5] Verblunsky S., “On an expansion in exponential series”, Quart. J. Math., 7:27 (1956), 231–240 | DOI | MR | Zbl