Geodesic
Linear functional equations
Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 357-370.

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

Necessary and sufficient conditions are found for the existence and uniqueness of local $C^\infty$ solutions of multidimensional linear functional equations of the form $$ \varphi(\Lambda x)-Q\varphi(x)=\gamma(x). $$ Sufficient conditions for local $C^\infty$ solvability are also obtained for equations with variable coefficients. Bibliography: 5 titles. 
@article{IM2_1978_12_2_a9,
     author = {L. P. Kuchko},
     title = {Linear functional equations},
     journal = {Izvestiya. Mathematics },
     pages = {357--370},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a9/}
}
TY  - JOUR
AU  - L. P. Kuchko
TI  - Linear functional equations
JO  - Izvestiya. Mathematics 
PY  - 1978
SP  - 357
EP  - 370
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a9/
LA  - en
ID  - IM2_1978_12_2_a9
ER  - 
%0 Journal Article
%A L. P. Kuchko
%T Linear functional equations
%J Izvestiya. Mathematics 
%D 1978
%P 357-370
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a9/
%G en
%F IM2_1978_12_2_a9
L. P. Kuchko. Linear functional equations. Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 357-370. http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a9/

[1] Belitskii G. R., “Funktsionalnye uravneniya i lokalnaya sopryazhennost otobrazhenii klassa $C^\infty$”, Matem. sb., 133:8 (1973), 565–579

[2] Kassels Dzh. V. S., Vvedenie v teoriyu diofantovykh priblizhenii, IL, M., 1961

[3] Kuchko L. P., “O lineinykh funktsionalnykh uravneniyakh”, Vestnik Kharkovskogo un-ta, ser. mekhaniko-matem., 39 (1974), 3–14 | Zbl

[4] Malgranzh B., Idealy differentsiruemykh funktsii, Mir, M., 1968

[5] Tychonoff A. N., “Ein Fixpunktsatz”, Math. Ann., 111:5 (1935), 767–776 | DOI | MR | Zbl