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Mat. Zametki, 2011 Volume 89, Issue 6, Pages 846–855 (Mi mzm8768)
Differential Operators Symmetric with Respect to an Indefinite Metric

R. S. Ismagilova, Sh. Sh. Sultanovb

a N. E. Bauman Moscow State Technical University
b Nizhnevartovsk State Humanitarian University

Abstract: 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.

UDC: 517.983

Received: 25.01.2010

DOI: 10.4213/mzm8768


 English version: Mathematical Notes, 2011, 89:6, 810–818

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© Steklov Math. Inst. of RAS, 2025