Estimates of Approximation Numbers and Completeness of Root Vectors of A Singular Operator Generated by the Linear Part of the Korteweg-de Vries Operator


Muratbekov M. Muratbekov M. Bayandiyev Y.
2026John Wiley and Sons Ltd

Mathematical Methods in the Applied Sciences
2026

We investigate a linear operator associated with the linear part of the Korteweg-de Vries operator on an unbounded domain with unbounded coefficients. The existence and compactness of the resolvent are established, along with separability results ensuring maximal regularity of solutions. Two-sided estimates are derived for the distribution function of approximation numbers, characterizing the rate of finite-dimensional approximation of the resolvent. The completeness of the system of root vectors is also proved, which plays a key role in the analysis of related nonlinear operators.

approximation numbers , Korteweg-de Vries operator , resolvent , root vectors , separability , singular numbers , singular operator

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Mathematics in Education, Taraz Regional University named after M.Kh. Dulaty (Dulaty University), Taraz, Kazakhstan
Information Security, L. N. Gumilyov Eurasian National University, Astana, Kazakhstan

Mathematics in Education
Information Security

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026