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 Mat. Zametki, 2018, Volume 104, Issue 3, Pages 374–395 (Mi mz12112)

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

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.

 Funding Agency Grant Number CONACYT - Consejo Nacional de Ciencia y Tecnología 238630 National Science Foundation DMS-1716975 The work of the first author was supported by the grant CONACYT 238630. The work of the second author was supported by the NSF award DMS-1716975.

DOI: https://doi.org/10.4213/mzm12112

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English version:
Mathematical Notes, 2018, 104:3, 377–394

Bibliographic databases:

UDC: 517.957+517.984.2

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), 374–395; Math. Notes, 104:3 (2018), 377–394

Citation in format AMSBIB
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