Geodesic
On Model Representations of Non-Selfadjoint Operators with Infinitely Dimensional Imaginary Component
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 2, pp. 174-186 
R. Hatamleh; V. A. Zolotarev. On Model Representations of Non-Selfadjoint Operators with Infinitely Dimensional Imaginary Component. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 2, pp. 174-186. http://geodesic.mathdoc.fr/item/JMAG_2015_11_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For an entirely non-selfadjoint operator with spectrum at zero, the imaginary component of which has an absolutely continuous spectrum (not necessarily dissipative and having lacunas in the spectrum), triangular and functional models are constructed.

[1] M. S. Livs̆ic, “On Spectral Decomposition of Linear Non-Selfadjoint Operators”, Matem. sb., 34/76:1 (1954), 145–198 (Russian)

[2] M. S. Livs̆ic, A. A. Yantsevich, Theory of Operator Colligations in Hilbert Spaces, Kharkov University Publishing House, Kharkov, 1971 (Russian)

[3] V. A. Zolotarev, Analitic Methods of Spectral Representations of Non-Selfadjoint and Nonunitary Operators, Kharkov University Publishing House, Kharkov, 2003 (Russian)

[4] B. Ya. Levin, Lectures on Entire Functions, Amer. Math. Soc., Providence, RI, 1996, 150 pp.

[5] N. I. Akhiezer, Lectures on Integral Transforms, Kharkov University Publishing House, Kharkov, 1984 (Russian)

[6] N. I. Akhiezer, I. M. Glazman, Theory of Linear Operators in Hilbert Space, v. 1, 2, Kharkov University Publishing House, Kharkov, 1978 (Russian)

[7] R. Hatamleh, V. A. Zolotarev, “On Many-Dimensional Model Representations of One Class of Commuting Operators”, Ukr. Math. Jornal, 66:1 (2014), 108–127