Literature cited
H. Langer, “Über stark gedampfte Scharen im Hilbertraum,” J. Math. Mech.,17, 685–706 (1968).
R. J. Duffin, “A minimax theory for overdamped networks,” J. Rat. Mech. Anal.,4, 221–223 (1955).
A. S. Markus, Introduction to the Spectral Theory of Polynomial Operator Pencils [in Russian], Shtinitsa, Kishinev (1986).
Yu. Sh. Abramov, Variational Methods in the Theory of Operator Pencils. Spectral Optimization [in Russian], Leningrad State Univ. (1983).
A. A. Shkalikov, “Strongly damped pencils of operators and solvability of the corresponding operator-differential equations,” Mat. Sb.,135, No. 1, 96–118 (1988).
A. S. Markus and V. I. Matsaev, “On the basicity of a certain part of the eigenvectors and associated vectors of a self-adjoint operator pencil,” Mat. Sb.,133, No. 3, 293–313 (1987).
T. Ya. Azizov, “Spectral theory and extension theory of operators in spaces with indefinite metric,” Doctoral Dissertation, Mathematics Institute, Academy of Sciences of the Ukrainian SSR, Kiev (1988).
M. V. Keldyshm, “On the completeness of the eigenfunctions of certain classes of nonself-adjoint linear operators,” Usp. Mat. Nauk,26, No. 4, 15–41 (1971).
A. G. Kostyuchenko and A. A. Shkalikov, “Self-adjoint quadratic pencils of operators and elliptic problems,” Funkts. Anal. Prilozhen.,17, No. 2, 38–61 (1983).
T. Ya. Azizov and I. S. Iokhvidov, Fundamentals of the Theory of Linear Operators in Spaces with an Indefinite Metric [in Russian], Nauka, Moscow (1986).
A. A. Shkalikov, “On the minimality of the derived chains corresponding to a part of the eigenelements and associated elements of self-adjoint operator pencils,” Vestn. Mosk. Gos. Univ., Ser.1, Mat. Mekh., No. 6, 10–18 (1985).
H. Langer, “Factorization of operator pencils,” Acta Scient. Math. Szeged.,38, No. 2, 83–96 (1976).
G. V. Radzievskii, “On the linear independence of the Keldysh-derived chains of analytic operator-valued functions in the halfplane,” Mat. Sb.,132, No. 4, 556–577 (1987).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 45, No. 2, pp. 118–128, February, 1989.
Rights and permissions
About this article
Cite this article
Shkalikov, A.A., Pliev, V.T. Compact perturbations of strongly damped operator pencils. Mathematical Notes of the Academy of Sciences of the USSR 45, 167–174 (1989). https://doi.org/10.1007/BF01158065
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01158065