On the trace-class property of Hankel operators arising in the theory of the Korteweg-de Vries equation

DOI10.1134/S0001434618090067OpenAlexW2901649387MaRDI QIDQ1731474

A. V. Rybkin, Sergei M. Grudsky

Publication date: 13 March 2019

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434618090067

zbMATH Keywords

trace-class operatorHankel operatorKorteweg-de Vries equationinverse problem method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35)

Related Items (2)

Realization of the inverse scattering transform method for the Korteweg–de Vries equation ⋮ Invertibility issues for Toeplitz plus Hankel operators and their close relatives

Cites Work

• Bounded solutions of KdV and non-periodic one-gap potentials in quantum mechanics
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• KdV equation beyond standard assumptions on initial data
• Spatial Analyticity of Solutions to Integrable Systems. I. The KdV Case
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• On Peller’s characterization of trace class Hankel operators and smoothness of KdV solutions
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• Some open problems in random matrix theory and the theory of integrable systems
• The Connection between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painlevé Type
• Solutions to the Korteweg–de Vries Equation with Initial Profile in $L_1^1 (\mathbb{R}) \cap L_N^1 (\mathbb{R}^ + )$
• HANKEL OPERATORS OF CLASS $ \mathfrak{S}_p$ AND THEIR APPLICATIONS (RATIONAL APPROXIMATION, GAUSSIAN PROCESSES, THE PROBLEM OF MAJORIZING OPERATORS)
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
• Inverse scattering on the line
• Method for Solving the Korteweg-deVries Equation
• Periodic and almost-periodic potentials in inverse problems
• Soliton Theory and Hankel Operators
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