Geodesic
Differential Operators Symmetric with Respect to an Indefinite Metric
Matematičeskie zametki, Tome 89 (2011) no. 6, pp. 846-855

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We describe classes of second-order differential operators on a circle that are symmetric with respect to an indefinite metric with a finite rank of indefiniteness.
Keywords: differential operator, complex Hilbert space, $J$-symmetric operator, indefinite metric, periodic function, Pontryagin space, Krein space. 
@article{MZM_2011_89_6_a4,
     author = {R. S. Ismagilov and Sh. Sh. Sultanov},
     title = {Differential {Operators} {Symmetric} with {Respect} to an {Indefinite} {Metric}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {846--855},
     publisher = {mathdoc},
     volume = {89},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_6_a4/}
}
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R. S. Ismagilov; Sh. Sh. Sultanov. Differential Operators Symmetric with Respect to an Indefinite Metric. Matematičeskie zametki, Tome 89 (2011) no. 6, pp. 846-855. http://geodesic.mathdoc.fr/item/MZM_2011_89_6_a4/