An analog of the Jordan--Dirichlet theorem for an operator with involution on a graph
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 17-24
Voir la notice de l'article provenant de la source Math-Net.Ru
In this paper, we examine the convergence of eigenfunction expansions of a functional-differential operator with involution $\nu(x)=1-x$, which is defined on a geometric graph consisting of two edges, one of which is a loop. Sufficient conditions are obtained for the uniform convergence of the Fourier series in the eigenfunctions of the operator (an analog of the Jordan–Dirichlet theorem).
Keywords:
functional-differential operator, involution, geometric graph, Fourier series.
@article{INTO_2021_193_a2,
author = {E. I. Biryukova},
title = {An analog of the {Jordan--Dirichlet} theorem for an operator with involution on a graph},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {17--24},
publisher = {mathdoc},
volume = {193},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2021_193_a2/}
}
TY - JOUR AU - E. I. Biryukova TI - An analog of the Jordan--Dirichlet theorem for an operator with involution on a graph JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2021 SP - 17 EP - 24 VL - 193 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2021_193_a2/ LA - ru ID - INTO_2021_193_a2 ER -
%0 Journal Article %A E. I. Biryukova %T An analog of the Jordan--Dirichlet theorem for an operator with involution on a graph %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2021 %P 17-24 %V 193 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2021_193_a2/ %G ru %F INTO_2021_193_a2
E. I. Biryukova. An analog of the Jordan--Dirichlet theorem for an operator with involution on a graph. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 17-24. http://geodesic.mathdoc.fr/item/INTO_2021_193_a2/