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Algebra i Analiz, 2018, Volume 30, Issue 3, Pages 286–310 (Mi aa1605)  
Research Papers

A new representation of Hankel operators and its spectral consequences

D. R. Yafaevab

a Univ Rennes, CNRS, IRMAR-UMR 6625, F-35000 Rennes, France
b St. Petersburg State University, Universitetskaya nab. 7/9, 199034, St. Petersburg, Russia
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Abstract: In the paper, the Hankel operators $H$ are represented as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of functions of a one variable only. This representation has numerous spectral consequences, both for compact Hankel operators and for operators with the continuous spectrum.
Keywords: Hankel operators, spectral properties, absolutely continuous and discrete spectra, asymptotics of eigenvalues.
Funding agency Grant number
Russian Science Foundation 17-11-01126
Supported by Russian Science Foundation, project № 17-11-01126.
Received: 12.12.2017
English version:
St. Petersburg Mathematical Journal, 2019, Volume 30, Issue 3, Pages 601–619
DOI: https://doi.org/10.1090/spmj/1561
Bibliographic databases:
Document Type: Article
MSC: 47A40, 47B06, 47B25, 47B35
Language: English
Citation: D. R. Yafaev, “A new representation of Hankel operators and its spectral consequences”, Algebra i Analiz, 30:3 (2018), 286–310; St. Petersburg Math. J., 30:3 (2019), 601–619
Citation in format AMSBIB
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