Geodesic
On finite dimensional and nuclear operators in Hardy spaces $H^2$ on compact Abelian groups
Problemy fiziki, matematiki i tehniki, no. 4 (2015), pp. 74-79

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Compact and connected Abelian group $G$ with totally ordered dual is considered. It is shown that nontrivial finite rank Hankel operator exists on $G$ if and only if the dual group contains the first positive element. In this case the classical theorems by Kroneker, Hartman, and Peller are generalized to the case of Hankel operators on $G$.
Keywords: compact Abelian group, Hankel operator, finite rank operator, nuclear operator. 
@article{PFMT_2015_4_a13,
     author = {A. R. Mirotin and R. V. Dyba},
     title = {On finite dimensional and nuclear operators in {Hardy} spaces $H^2$ on compact {Abelian} groups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {74--79},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_4_a13/}
}
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A. R. Mirotin; R. V. Dyba. On finite dimensional and nuclear operators in Hardy spaces $H^2$ on compact Abelian groups. Problemy fiziki, matematiki i tehniki, no. 4 (2015), pp. 74-79. http://geodesic.mathdoc.fr/item/PFMT_2015_4_a13/