Geodesic
Estimation of resolvents for discrete weighted shift operators
Problemy fiziki, matematiki i tehniki, no. 1 (2015), pp. 48-52.

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

A lower estimation for the norm of a resolvent operator, the spectrum of which is a unite circle is considered. It is shown that for arbitrary function $\varphi(\lambda)$, that is analytic on a unit circle, there exist an operator such that its resolvent norm is greater than $|\varphi(\lambda)|$.
Keywords: resolvent, discrete weighted shift operator. 
@article{PFMT_2015_1_a8,
     author = {A. B. Antonevich and Ali A. Shukur},
     title = {Estimation of resolvents for discrete weighted shift operators},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {48--52},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_1_a8/}
}
TY  - JOUR
AU  - A. B. Antonevich
AU  - Ali A. Shukur
TI  - Estimation of resolvents for discrete weighted shift operators
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2015
SP  - 48
EP  - 52
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2015_1_a8/
LA  - ru
ID  - PFMT_2015_1_a8
ER  - 
%0 Journal Article
%A A. B. Antonevich
%A Ali A. Shukur
%T Estimation of resolvents for discrete weighted shift operators
%J Problemy fiziki, matematiki i tehniki
%D 2015
%P 48-52
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2015_1_a8/
%G ru
%F PFMT_2015_1_a8
A. B. Antonevich; Ali A. Shukur. Estimation of resolvents for discrete weighted shift operators. Problemy fiziki, matematiki i tehniki, no. 1 (2015), pp. 48-52. http://geodesic.mathdoc.fr/item/PFMT_2015_1_a8/

[1] A. B. Antonevich, Lineinye funktsionalnye uravneniya. Operatornyi podkhod, Universitetskoe, Minsk, 1988, 230 pp.

[2] N. Danford, Dzh. Shvarts, Lineinye operatory. Spektralnaya teoriya, Mir, M., 1966, 896 pp.

[3] G. G. Magaril-Ilyaev, V. M. Tikhomirov, Vypuklyi analiz i ego prilozheniya, Knizhnyi dom «Liberkom», M., 2011, 172 pp.

[4] P. P. Zabrejko, “Error estimates for successive approximations and spectral properties of linear operators”, Numerical functional analysis and optimization, 11:788 (1990), 823–838 | DOI

[5] O. Nevanlinna, “On growth of the resolvent operators for power bounded operators”, Banach center publications, 38, Warszawa, 1997, 18 pp.

[6] O. Nevanlinna, Resolvent conditions and powers of operators, Helsinki university of technology Institute of mathematies research reports, , 1999 (Data of access: 10.05.2014) https://math.aalto.fi/reports/a424.pdf