Estimates of Approximation Numbers, Nuclearity of the Resolvent of a Third-Order Singular Differential Operator, and the Completeness of Its Root Vectors
Muratbekov M. Muratbekov M. Shuitenov G.
30 May 2025John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2025#48Issue 88903 - 8910 pp.
In this paper, we examine a third-order singular differential operator in the space (Formula presented.), with a coefficient which is a continuous function on (Formula presented.) and exhibits potential growth at infinity. We prove the existence of the operators resolvent and establish the maximal regularity of the solutions to the equation associated with the operator. We also prove the compactness property of the resolvent and obtain two-sided bounds for the singular numbers (s-numbers). These bounds provide the rate at which the resolvent of the operator under consideration can be approximated by finite-dimensional linear operators. To the best of our knowledge, we establish for the first time the nuclearity of the resolvent for a third-order differential operator and demonstrate the completeness of the operators root vectors in the case of an unbounded domain with a rapidly growing coefficient at infinity.
approximation numbers , completeness of root vectors , nuclearity , resolvent , separability , singular operator , third-order differential 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
Department of Information Systems and Technologies, Esil University, Astana, Kazakhstan
Mathematics in Education
Information Security
Department of Information Systems and Technologies
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