Literature cited
Yu. M. Berezanskii, Eigenfunction Expansions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
M. L. Gorbachuk and A. N. Kochubei, “Self-adjoint boundary value problems for certain classes of differential operator equations of high order,” Dokl. Akad. Nauk SSSR, 201, No. 5 (1971).
M. G. Gimadislamov, “On the conditions for the self-adjointness of a differential operator of a higher order with an operator coefficient,” Matem. Zametki,5, No. 6 (1969).
L. I. Vainerman and M. L. Gorbachuk, “Direct methods of qualitative spectral analysis of a singular Sturm —Liouville equation with an unbounded operator potential,” Dop, Akad. Nauk UkrRSR, Ser. A, No. 7 (1972).
I. M. Glazman, Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators [in Russian], Fizmatgiz, Moscow (1963).
F. Riesz and B. Sz.-Nagy, Lectures on Functional Analysis [Russian translation], IL, Moscow (1954).
G. H. Hardy, J. Littlewood, and G. Polya, Inequalities [Russian translation], IL, Moscow (1948).
M. Sh. Birman, “On the spectrum of singular boundary value problems,” Matem. Sb.,55, No. 2 (1961).
B. M. Levitan and G. A. Suvorchenkova, “Sufficient conditions for the discreteness of the spectrum of a Sturm-Liouville equation with an operator coefficient,” Funktsional. Analiz i Ego Prilozhen.,2, No. 2 (1968).
V. P. Maslov, “On a criterion for the discreteness of the spectrum of a Sturm —Liouville equation with an operator coefficient,” Funktsional. Analiz i Ego Prilozhen.,2, No. 2 (1968).
M. M. Alekberli, “Sufficient conditions for the discreteness of the spectrum of a self-adjoint differential operator of order 2n, ” in: Scientific Communications (on Natural and Technical Sciences) [in Russian], Part 2, Dagestanskii Univ., Makhachkala (1970).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 26, No. 6, PP. 811–815, November–December, 1973.
In conclusion the author expresses his thanks to M. L. Gorbachuk for supervising this work, and to L. I. Vainerman for useful discussions.
Rights and permissions
About this article
Cite this article
Kochubei, A.N. On the self-adjointness and on the nature of the spectrum of certain classes of abstract differential operators. Ukr Math J 25, 673–676 (1973). https://doi.org/10.1007/BF01090802
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01090802