Remarks on the application of the Keldysh theorem to the completeness of root subspace of non-self-adjoint operators and comments on "Spectral operators generated by Timoshenko beam model"

Bao Zhu Guo; Jun Min Wang

doi:10.1016/j.sysconle.2006.06.016

Remarks on the application of the Keldysh theorem to the completeness of root subspace of non-self-adjoint operators and comments on "Spectral operators generated by Timoshenko beam model"

Bao Zhu Guo^*
, Jun Min Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this note, we show, by means of an example, that the assumption of compactness in the Keldysh theorem in proving the completeness of root subspaces of non-self-adjoint operators cannot be ignored. This indicates a gap of the above mentioned paper and many other related papers in the proof of completeness for the root subspaces of beam-related problems.

Original language	English
Pages (from-to)	1029-1032
Number of pages	4
Journal	Systems and Control Letters
Volume	55
Issue number	12
DOIs	https://doi.org/10.1016/j.sysconle.2006.06.016
Publication status	Published - Dec 2006
Externally published	Yes

Keywords

Completeness
Generalized eigenvectors
Keldysh theorem
Root subspace

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10.1016/j.sysconle.2006.06.016

Cite this

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title = "Remarks on the application of the Keldysh theorem to the completeness of root subspace of non-self-adjoint operators and comments on {"}Spectral operators generated by Timoshenko beam model{"}",

abstract = "In this note, we show, by means of an example, that the assumption of compactness in the Keldysh theorem in proving the completeness of root subspaces of non-self-adjoint operators cannot be ignored. This indicates a gap of the above mentioned paper and many other related papers in the proof of completeness for the root subspaces of beam-related problems.",

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AU - Guo, Bao Zhu

AU - Wang, Jun Min

PY - 2006/12

Y1 - 2006/12

N2 - In this note, we show, by means of an example, that the assumption of compactness in the Keldysh theorem in proving the completeness of root subspaces of non-self-adjoint operators cannot be ignored. This indicates a gap of the above mentioned paper and many other related papers in the proof of completeness for the root subspaces of beam-related problems.

AB - In this note, we show, by means of an example, that the assumption of compactness in the Keldysh theorem in proving the completeness of root subspaces of non-self-adjoint operators cannot be ignored. This indicates a gap of the above mentioned paper and many other related papers in the proof of completeness for the root subspaces of beam-related problems.

KW - Completeness

KW - Generalized eigenvectors

KW - Keldysh theorem

KW - Root subspace

UR - https://www.scopus.com/pages/publications/33750024796

U2 - 10.1016/j.sysconle.2006.06.016

DO - 10.1016/j.sysconle.2006.06.016

M3 - Article

AN - SCOPUS:33750024796

SN - 0167-6911

VL - 55

SP - 1029

EP - 1032

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 12

ER -

Remarks on the application of the Keldysh theorem to the completeness of root subspace of non-self-adjoint operators and comments on "Spectral operators generated by Timoshenko beam model"

Abstract

Keywords

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