On the Trace-Class Property of Hankel Operators Arising in the Theory of the Korteweg–de Vries Equation

On the Trace-Class Property of Hankel Operators Arising in the Theory of the Korteweg–de Vries Equation

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...

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Veröffentlicht in:Mathematical Notes 2018-09, Vol.104 (3-4), p.377-394
Hauptverfasser: Grudsky, S. M., Rybkin, A. V.
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Sprache:eng
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Cauchy problems
Korteweg-Devries equation
Mathematics
Mathematics and Statistics
Operators (mathematics)
Saddle points
Smoothness
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description 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.
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subjects Cauchy problems
Korteweg-Devries equation
Mathematics
Mathematics and Statistics
Operators (mathematics)
Saddle points
Smoothness
title On the Trace-Class Property of Hankel Operators Arising in the Theory of the Korteweg–de Vries Equation
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