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Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 5

Normal Differential Operators of Third Order

M. EROL
Z. I. ISMAILOV
Pages
675–688
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In particular, thecase of A−1 ∈ S∞(H), asymptotic estimates of normal extensions ofeigenvalues has been established at infinity.

📌 3 Key Takeaways

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Objective & Hypothesis:In the Hilbert space of vector-functions L2(H,(a, b)), where H is anyseparable Hilbert space, the general representation in terms of boundary values of all normal extensions of the formally normal minimaloperator, generated by linear differential-operator expressions of thirdorder in the forml(u) = u′′′(t) + A3u(t), A : D(A) ⊂ H → H, A = A∗ ≥ E,is obtained in the first part of this study.
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Key Findings & Data:Then, some spectral properties of these normal extensions are investigated.
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Conclusion & Impact:In particular, thecase of A−1 ∈ S∞(H), asymptotic estimates of normal extensions ofeigenvalues has been established at infinity.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Normal extension · Compact operator · Eigenvalue

Abstract

In the Hilbert space of vector-functions L2(H,(a, b)), where H is anyseparable Hilbert space, the general representation in terms of boundary values of all normal extensions of the formally normal minimaloperator, generated by linear differential-operator expressions of thirdorder in the forml(u) = u′′′(t) + A3u(t), A : D(A) ⊂ H → H, A = A∗ ≥ E,is obtained in the first part of this study. Then, some spectral properties of these normal extensions are investigated. In particular, thecase of A−1 ∈ S∞(H), asymptotic estimates of normal extensions ofeigenvalues has been established at infinity.

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Cite This Article

EROL, M., ISMAILOV, Z. I. (2022). Normal Differential Operators of Third Order. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 5, 675–688. https://ajindex.com/articles/530467

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