Geodesic
Properties and description of solution sets of linear functional equations on a simple smooth curve
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 4, pp. 5-13

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

The article investigates linear functional equations given in the field of complex numbers on simple smooth curves with a shift function of infinite order. The shift function has a nonzero derivative satisfying the Helder condition, and fixed points only at the ends of the curve. The paper gives a complete description of the sets of solutions of such equations in the classes of continuous, Helder, and primitive Lebesgue functions with a coefficient and the right side of the same classes, depending on the values of the coefficient of the equation at the ends of the curve. Sufficient conditions have been established for the solutions to belong to the specified functional classes.
Keywords: singular integral equations with shift, linear functional equations from one variable, Helder function classes
Mots-clés : classes of primitives from Lebesgue functions. 
@article{VYURM_2023_15_4_a0,
     author = {V. L. Dilman},
     title = {Properties and description of solution sets of linear functional equations on a simple smooth curve},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {5--13},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2023_15_4_a0/}
}
TY  - JOUR
AU  - V. L. Dilman
TI  - Properties and description of solution sets of linear functional equations on a simple smooth curve
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2023
SP  - 5
EP  - 13
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURM_2023_15_4_a0/
LA  - ru
ID  - VYURM_2023_15_4_a0
ER  - 
%0 Journal Article
%A V. L. Dilman
%T Properties and description of solution sets of linear functional equations on a simple smooth curve
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2023
%P 5-13
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURM_2023_15_4_a0/
%G ru
%F VYURM_2023_15_4_a0
V. L. Dilman. Properties and description of solution sets of linear functional equations on a simple smooth curve. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 4, pp. 5-13. http://geodesic.mathdoc.fr/item/VYURM_2023_15_4_a0/