×

On J-selfadjoint extensions of J-symmetric ordinary differential operators. (English) Zbl 0664.34037

The author gives three characterizations of the boundary conditions which determine the domain of any J-selfadjoint extension of a concrete J- symmetric ordinary differential operator on (a,b) in case when the endpoint a is regular or singular and the endpoint b is singular.
Reviewer: J.Kalinowski

MSC:

34L99 Ordinary differential operators
47E05 General theory of ordinary differential operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Zhi-jiang, Cao, On selfadjoint extensions of \(n\) th order differential operators in the limitcircle case, Acta Math. Sinica, 28, 205-217 (1985), [Chinese]
[2] Zhi-jiang, Cao; Jiong, Sun, Self-adjoint operators generated by symmetric quasi-differential expressions, Acta Sci. Natur. Univ. Intramongolicae, 17, 7-15 (1986), [Chinese] · Zbl 1332.47019
[3] Dunford, N.; Schwartz, J. T., Linear Operators (1963), Interscience: Interscience New York, Part II
[4] Everitt, W. N.; Zettl, A., Generalised symmetric ordinary differential expressions. I. The general theory, Nieuw Arch. Wisk., 27, 363-397 (1979), (3) · Zbl 0451.34009
[5] Galindo, A., On the existence of \(J\)-selfadjoint extensions of \(J\)-symmetric operators with adjoint, Comm. Pure Appl. Math., 15, 423-425 (1963) · Zbl 0109.08701
[6] Glazman, I. M., An analogue of the extension theory of hermitian operators and of the non-symmetric one dimensional boundary value problem on a semi-axis, Dokl. Akad. Nauk SSSR, 115, 214-216 (1957), [Russian] · Zbl 0079.33102
[7] Kauffman, R. M.; Read, T. T.; Zettl, A., The Deficiency Index Problem for Powers of Ordinary Differential Expressions, (Lecture Notes in Mathematics, Vol. 621 (1977), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0367.34014
[8] Knowles, I., On \(J\)-selfadjoint extensions of \(J\)-symmetric operators, (Proc. Amer. Math. Soc., 79 (1980)), 42-44 · Zbl 0443.47035
[9] Knowles, I., On the boundary conditions characterizing \(J\)-selfadjoint extensions of \(J\)-symmetric operators, J. Differential Equations, 40, 193-216 (1981) · Zbl 0483.34019
[10] Naimark, M. A., Linear Differential Operators (1954), GITTL: GITTL Moscow, [Russian] · Zbl 0057.07102
[11] Race, D., The theory of \(J\)-selfadjoint extensions of \(J\)-symmetric operators, J. Differential Equations, 57, 258-274 (1985) · Zbl 0525.47016
[13] Zai-jiu, Shang; Rui-ying, Zhu, The domains of selfadjoint extensions of ordinary symmetric differential operators over (−∞, +∞), Acta Sci. Natur. Univ. Intramongolicae, 17, 17-28 (1986), [Chinese] · Zbl 1332.47024
[14] Zettl, A., Formally self-adjoint quasi-differential operators, Rocky Mountain J. Math., 5, 453-474 (1975) · Zbl 0443.34019
[15] Zhikhar, N. A., The theory of extensions of \(J\)-symmetric operators, Ukrain. Mat. Zh., 11, 352-364 (1959), [Russian] · Zbl 0113.31601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.