Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single and direct sum Hilbert spaces.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, regular and singular fourth order differential operators with distributional potentials are investigated.
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Key Findings & Data:In particular, existence and uniqueness of solutions of the fourth order differential equations are proved, deficiency indices theory of the corresponding minimal symmetric operators are studied.
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Conclusion & Impact:Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single and direct sum Hilbert spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Distributional potentials · deficiency indices · extension theory
Abstract
In this paper, regular and singular fourth order differential operators with distributional potentials are investigated. In particular, existence and uniqueness of solutions of the fourth order differential equations are proved, deficiency indices theory of the corresponding minimal symmetric operators are studied. These symmetric operators are considered as acting on the single and direct sum Hilbert spaces. The latter one consists of three Hilbert spaces such that a squarely integrable space and two spaces of complex numbers. Moreover all maximal self-adjoint, maximal dissipative and maximal accumulative extensions of the minimal symmetric operators including direct sum operators are given in the single and direct sum Hilbert spaces.
UĞURLU, E., BAIRAMOV, E. (2020). Fourth order differential operators with distributional potentials. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 3, 825–856. https://ajindex.com/articles/193189
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