Geodesic
Hilbert space unconditional bases formed by values of an entire vector-function of order~1/2
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 30, Tome 290 (2002), pp. 33-41

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Let $B$ a dissipative Volterra operator in a separable Hilbert space $\mathfrak H$ such that the resolvent $(I-zB)^{-1}$ has finite exponential type. A complete description is given of the operators $B$ with the above properties, vectors $g\in\mathfrak H$, and sequences $\Lambda$ of complex numbers such that the family $$ (I-\lambda_kB^2)^{-1}, \quad \lambda_k\in\Lambda, $$ forms an unconditional basis in $\mathfrak H$. 
@article{ZNSL_2002_290_a2,
     author = {G. M. Gubreev and M. G. Volkova},
     title = {Hilbert space unconditional bases formed by values of an entire vector-function of order~1/2},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--41},
     publisher = {mathdoc},
     volume = {290},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a2/}
}
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G. M. Gubreev; M. G. Volkova. Hilbert space unconditional bases formed by values of an entire vector-function of order~1/2. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 30, Tome 290 (2002), pp. 33-41. http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a2/