Geodesic
Root lineals and characteristic functions of contractions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 155-158 
M. S. Brodskii; Ya. S. Shvartsman. Root lineals and characteristic functions of contractions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 155-158. http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a9/
@article{ZNSL_1974_47_a9,
     author = {M. S. Brodskii and Ya. S. Shvartsman},
     title = {Root lineals and characteristic functions of contractions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {155--158},
     year = {1974},
     volume = {47},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a9/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is proved that $\operatorname{dim}\operatorname{Ker}(T-\lambda I)^n=\operatorname{dim}\operatorname{Ker}K_n(\lambda)$, where $T$ is a contraction of the Hilbert space, $$ K_n(\lambda) =\begin{pmatrix} \theta^{*}(\bar\lambda)&0&\dots&0\\ \frac1{1!}\theta^{*(1)}(\bar\lambda)&\theta^{*}(\bar\lambda)&\dots&0\\ \frac1{(n-1)!}\theta^{*(n-1)}(\bar\lambda)&\frac1{(n-2)!}\theta^{*(n-2)}(\bar\lambda)&\dots& \theta^{*}(\bar\lambda) \end{pmatrix}, $$ $\theta$ – the characteristic function of the operator collegation generated by the contraction $T$.