On Peller’s characterization of trace class Hankel operators and smoothness of KdV solutions
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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.References
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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
- 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
- Communicated by: Joachim Krieger
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1627-1637
- MSC (2010): Primary 34B20, 37K15, 47B35
- DOI: https://doi.org/10.1090/proc/13844
- MathSciNet review: 3754347
Dedicated: This paper is dedicated to the memory of Ludwig Faddeev, one of the founders of soliton theory