It is shown that the system of eigenfunctions of considered problem forms a basis for Gp)(−1; 1), 1 < p < +∞, after removal of any of its even-numbered functions.
📌 3 Key Takeaways
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Objective & Hypothesis:Basicity of the system of eigenfunctions of some discontinuous spectral problem for a second order differential equation with spectral parameter in boundary condition for grand-Lebesgue space Lp)(−1; 1) is studied in this work.
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Key Findings & Data:The subspace Gp)(−1; 1) of Lp)(−1; 1) generated by shift operator is considered.
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Conclusion & Impact:It is shown that the system of eigenfunctions of considered problem forms a basis for Gp)(−1; 1), 1 < p < +∞, after removal of any of its even-numbered functions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Basicity of the system of eigenfunctions of some discontinuous spectral problem for a second order differential equation with spectral parameter in boundary condition for grand-Lebesgue space Lp)(−1; 1) is studied in this work. Since the space is nonseparable, a subspace suitable for the spectral problem is defined. The subspace Gp)(−1; 1) of Lp)(−1; 1) generated by shift operator is considered. Basicity of the system of eigenfunctions for the space Gp)(−1; 1)⊕C , 1 < p < +∞, is proved. It is shown that the system of eigenfunctions of considered problem forms a basis for Gp)(−1; 1), 1 < p < +∞, after removal of any of its even-numbered functions.
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Cite This Article
ŞİRİN, F., ZEREN, Y., ISMAILOV, M. (2022). On basicity of the system of eigenfunctions of one discontinuous spectral problem for second order differential equation for grand-Lebesgue space. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 5, 1595–1611. https://ajindex.com/articles/607888
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