Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 30, Tome 290 (2002), pp. 33-41
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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/
@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},
year = {2002},
volume = {290},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a2/}
}
TY - JOUR
AU - G. M. Gubreev
AU - M. G. Volkova
TI - Hilbert space unconditional bases formed by values of an entire vector-function of order 1/2
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2002
SP - 33
EP - 41
VL - 290
UR - http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a2/
LA - ru
ID - ZNSL_2002_290_a2
ER -
%0 Journal Article
%A G. M. Gubreev
%A M. G. Volkova
%T Hilbert space unconditional bases formed by values of an entire vector-function of order 1/2
%J Zapiski Nauchnykh Seminarov POMI
%D 2002
%P 33-41
%V 290
%U http://geodesic.mathdoc.fr/item/ZNSL_2002_290_a2/
%G ru
%F ZNSL_2002_290_a2
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 $\mathfrak H$.
