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On the Trace-Class Property of Hankel Operators Arising in the Theory of the Korteweg–de Vries Equation S. M. Grudskya, A. V. Rybkinb a Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional b University of Alaska Fairbanks Abstract: The trace-class property of Hankel operators (and their derivatives with respect to the parameter) with strongly oscillating symbol is studied. The approach used is based on Peller's criterion for the trace-class property of Hankel operators and on the precise analysis of the arising triple integral using the saddle-point method. Apparently, the obtained results are optimal. They are used to study the Cauchy problem for the Korteweg–de Vries equation. Namely, a connection between the smoothness of the solution and the rate of decrease of the initial data at positive infinity is established. Keywords: Hankel operator, trace-class operator, Korteweg–de Vries equation, inverse problem method.
DOI: https://doi.org/10.4213/mzm12112   Full text:
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English version: Mathematical Notes, 2018, 104:3, Bibliographic databases:   
UDC: 517.957+517.984.2 Received: 05.02.2018 Citation: S. M. Grudsky, A. V. Rybkin, “On the Trace-Class Property of Hankel Operators Arising in the Theory of the Korteweg–de Vries Equation”, Mat. Zametki, 104:3 (2018), 
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