SavedAdd your journal

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

Normal Differential Operators of Third Order

Z.i. Ismailov
M. Erol
Pages
—
Publication Date
2012-05-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:Then, some spectral properties of these normal extensions are investigated.
💡
Conclusion & Impact:In particular, the case of A −1 ∈ S∞(H), asymptotic estimates of normal extensions of eigenvalues 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 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.

🔖

Cite This Article

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

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. Albeverio, S., Gesztesy, F., Hoegh-Kron, R. and Holden, H. Sovable models in quantum mechanics(Springer, New York, Berlin, 1988).
  2. Coddington, E. A. Extension theory of formally normal and symmetric subspaces, Mem. Amer. Math. Soc. 134, 1–80, 1973.
  3. Edmunds, D. E. and Evans, W. D. Spectral Theory and Differential Operators (Clarendon Press, Oxford, 1990).
  4. Giaquinta, M. and Hildebrand, S. Calculus of Variations I (Springer-Verlang, Berlin, Hei- delberg, 2004).
  5. Gorbachuk, M. L. Self-adjoint boundary value problems for the differential equations for sec- ond order with the unbounded operator coefficient, Functional Analysis and its Applications (Moscow) 5 (1), 10–21, 1971 (in Russian).
  6. Gorbachuk, V. I. and Gorbachuk, M. L. Boundary Value Problems for Operator Differential Equations(Kluwer Academic Publisher, Dordrecht, 1991).
  7. Ismailov, Z. I. On the discreteness of the spectrum of normal differential operators for second order, Doklady NAS of Belarus 49 (3), 5–7, 2005.
  8. Ismailov, Z. I. Compact inverses of first-order normal differential operators, J. Math. Anal. App. USA 320 (1), 266–278, 2006.
  9. Rofe-Beketov, F. S. and Kholkin, A. M. Spectral theory of differential operators (World Sci- entific Monograph Series in Matmetics 7, New York, 2005).
  10. Yakubov, S. and Yakubov, Y. Diffrential Operator Equations Ordinary and Partial Differ
  11. ential Equations(Chapman&Hall/CRC, USA, 1999).