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

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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/}
}
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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/