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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 41 Issue: 5

Normal Differential Operators of Third Order

Z.i. Ismailov
M. Erol
Sayfa
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Yayın Tarihi
2012-05-01
DOI
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In particular, the case of A −1 ∈ S∞(H), asymptotic estimates of normal extensions of eigenvalues has been established at infinity.

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Amaç & Hipotez:In the Hilbert space of vector-functions L 2 (H,(a, b)), where H is any separable Hilbert space, the general representation in terms of boundary values of all normal extensions of the formally normal minimal operator, generated by linear differential-operator expressions of third order in the form l(u) = u ′′′(t) + A 3 u(t), A : D(A) ⊂ H → H, A = A ∗ ≥ E, is obtained in the first part of this study.
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Temel Bulgular & Veri:Then, some spectral properties of these normal extensions are investigated.
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Sonuç & Katkı:In particular, the case of A −1 ∈ S∞(H), asymptotic estimates of normal extensions of eigenvalues has been established at infinity.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Normal extension · Compact operator · Eigenvalue

Abstract

In the Hilbert space of vector-functions L 2 (H,(a, b)), where H is any separable Hilbert space, the general representation in terms of boundary values of all normal extensions of the formally normal minimal operator, generated by linear differential-operator expressions of third order in the form l(u) = u ′′′(t) + A 3 u(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, the case of A −1 ∈ S∞(H), asymptotic estimates of normal extensions of eigenvalues has been established at infinity.

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Bu Makaleye Atıf Yap

Ismailov, Z., Erol, M. (2012). Normal Differential Operators of Third Order. Hacettepe Journal of Mathematics and Statistics, Volume: 41 Issue: 5. https://ajindex.com/articles/1403517

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Kaynakça (11)

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