Geodesic
New convergence mode for the generalized spectrum
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 409-416

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

In this paper, we introduce a new convergence mode to deal with the generalized spectrum approximation of two bounded operators. This new technique is obtained by extending the well-known $\nu$-convergence used in the case of classical spectrum approximation. This new vision allows us to see the $\nu$-convergence assumption as a special case of our new method compared to the hypotheses needed in old methods, those required in this paper are weaker. In addition, we prove that the property $U$ holds, which solves the spectral pollution problem arising in spectrum approximation of unbounded operator. 
@article{SJVM_2022_25_4_a5,
     author = {S. Kamouche and H. Guebbai},
     title = {New convergence mode for the generalized spectrum},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {409--416},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a5/}
}
TY  - JOUR
AU  - S. Kamouche
AU  - H. Guebbai
TI  - New convergence mode for the generalized spectrum
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2022
SP  - 409
EP  - 416
VL  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a5/
LA  - ru
ID  - SJVM_2022_25_4_a5
ER  - 
%0 Journal Article
%A S. Kamouche
%A H. Guebbai
%T New convergence mode for the generalized spectrum
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2022
%P 409-416
%V 25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a5/
%G ru
%F SJVM_2022_25_4_a5
S. Kamouche; H. Guebbai. New convergence mode for the generalized spectrum. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 409-416. http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a5/