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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

A new representation of Hankel operators and its spectral consequences


Author: D. R. Yafaev
Original publication: Algebra i Analiz, tom 30 (2018), nomer 3.
Journal: St. Petersburg Math. J. 30 (2019), 601-619
MSC (2010): Primary 47A40, 47B06, 47B25, 47B35
DOI: https://doi.org/10.1090/spmj/1561
Published electronically: April 12, 2019
MathSciNet review: 3812009
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

D. R. Yafaev
Affiliation: Univ Rennes, CNRS, IRMAR–UMR 6625, F-35000 Rennes, France; and St. Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia
Email: yafaev@univ-rennes1.fr

DOI: https://doi.org/10.1090/spmj/1561
Keywords: Hankel operators, spectral properties, absolutely continuous and discrete spectra, asymptotics of eigenvalues
Received by editor(s): December 12, 2017
Published electronically: April 12, 2019
Additional Notes: Supported by Russian Science Foundation, project no. 17-11-01126
Dedicated: To the memory of Mikhail Zakharovich Solomyak
Article copyright: © Copyright 2019 American Mathematical Society