About kernel of inverse operator L' to third-order derivative's Ly = −y+q(x)y operator
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Date
2011
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Suleyman Demirel University
Abstract
This article investigates the kernel of the inverse operator associated with the third-order differential operator defined by Ly = −y'' + q(x)y under periodic-type boundary conditions. Using Kolmogorov widths and s-number theory, we establish estimates for the operator’s properties and demonstrate that the inverse operator is a kernel operator when q(x) is continuous and satisfies q(x) ≥ 1. Several supporting lemmas are proven, including inequalities for the operator and relationships between s-numbers and Kolmogorov widths. The results provide a theoretical framework for understanding the behavior of higher-order differential operators in Hilbert and Banach spaces.
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Keywords
Third-order differential operator, inverse operator, kernel operator, Kolmogorov widths, periodic boundary conditions
Citation
Omer Cakir /About kernel of inverse operator L' to third-order derivative's Ly = −y+q(x)y operator / Suleyman Demirel University/ СДУ хабаршысы, 2(18).