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Spectral analysis of a fourth order differential operator with periodic and antiperiodic boundary conditions


Author: D. M. Polyakov
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 27 (2015), nomer 5.
Journal: St. Petersburg Math. J. 27 (2016), 789-811
MSC (2010): Primary 34L20
DOI: https://doi.org/10.1090/spmj/1417
Published electronically: July 26, 2016
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Abstract: By the method of similar operators, the spectral properties of a fourth order differential operator are studied under periodic or semiperiodic boundary conditions. The spectrum asymptotics is obtained, together with some estimates for the spectral resolution for the operator in question. Also, the operator semigroup is constructed whose generator is equal to minus the operator under study.


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Additional Information

D. M. Polyakov
Affiliation: Institute of Mathematics, Voronezh State University, Universitetskaya pl. 1, Voronezh 394006, Russia
Email: DmitryPolyakow@mail.ru

DOI: https://doi.org/10.1090/spmj/1417
Keywords: Spectrum of an operator, fourth order differential operator, spectrum asymptotics, equiconvergence of spectral resolutions, method of similar operators
Received by editor(s): October 21, 2014
Published electronically: July 26, 2016
Additional Notes: Supported by RFBR (grants 14-01-31196 and 15-31-20241) and by RSF (grant 14-21-00066; Section 4) for investigations done at the Voronezh State University
Article copyright: © Copyright 2016 American Mathematical Society