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On Peller's characterization of trace class Hankel operators and smoothness of KdV solutions


Author: Alexei Rybkin
Journal: Proc. Amer. Math. Soc. 146 (2018), 1627-1637
MSC (2010): Primary 34B20, 37K15, 47B35
DOI: https://doi.org/10.1090/proc/13844
Published electronically: November 7, 2017
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Abstract: In the context of the Cauchy problem for the Korteweg-de Vries equation we put forward a new effective method to link smoothness of the solution with the rate of decay of the initial data. Our approach is based on the Peller characterization of trace class Hankel operators.


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Additional Information

Alexei Rybkin
Affiliation: Department of Mathematics and Statistics, University of Alaska Fairbanks, P.O. Box 756660, Fairbanks, Alaska 99775
Email: arybkin@alaska.edu

DOI: https://doi.org/10.1090/proc/13844
Keywords: KdV equation, Hankel operators.
Received by editor(s): April 21, 2017
Received by editor(s) in revised form: May 21, 2017
Published electronically: November 7, 2017
Additional Notes: The author was supported in part by the NSF grant DMS-1411560
Dedicated: This paper is dedicated to the memory of Ludwig Faddeev, one of the founders of soliton theory
Communicated by: Joachim Krieger
Article copyright: © Copyright 2017 American Mathematical Society

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