Geodesic
Eigenvector bases of completely nonunitary contractions and the characteristic function
Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 91-134

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We study Bari and Riesz bases $({}^1)$ of eigenspaces of contraction operators which are close to unitary. Subject to certain assumptions about the operator, we partition its spectrum into so-called Carleson series, in terms of which we establish new criteria for the basicity of the operator. Most completely studied are contractions with finite-dimensional deficiency operators $I-T^*T$ and $I-TT^*$. As examples we consider classical bases of exponential functions in various function spaces. 
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     author = {N. K. Nikol'skii and B. S. Pavlov},
     title = {Eigenvector bases of completely nonunitary contractions and the characteristic function},
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N. K. Nikol'skii; B. S. Pavlov. Eigenvector bases of completely nonunitary contractions and the characteristic function. Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 91-134. http://geodesic.mathdoc.fr/item/IM2_1970_4_1_a5/