Bulletin of the American Mathematical Society

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Book Information:

Author: A. S. Markus
Title: Introduction to the spectral theory of polynomial operator pencils
Additional book information: Translated by H. H. McFaden, Translations of Mathematical Monographs, vol. 71, American Mathematical Society, Providence, R.I., 1988, iv + 250 pp., $95.00. ISBN 0-8218-4523-3.

1.

M. V. Keldysh, On the eigenvalues and eigenfunctions of certain classes of nonselfadjoint equations, Dokl. Akad. Nauk SSSR 77 (1951), 11-14.

M. V. Keldyš, The completeness of eigenfunctions of certain classes of nonselfadjoint linear operators, Uspehi Mat. Nauk 26 (1971), no. 4(160), 15–41 (Russian). MR 0300125

I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by A. Feinstein. MR 0246142

M. G. Kreĭn and G. K. Langer, On the theory of quadratic pencils of self-adjoint operators, Dokl. Akad. Nauk SSSR 154 (1964), 1258–1261 (Russian). MR 0169060

M. G. Kreĭn and H. Langer, On some mathematical principles in the linear theory of damped oscillations of continua. I, Integral Equations Operator Theory 1 (1978), no. 3, 364–399. Translated from the Russian by R. Troelstra. MR 511976, DOI 10.1007/BF01682844

Leiba Rodman, An introduction to operator polynomials, Operator Theory: Advances and Applications, vol. 38, Birkhäuser Verlag, Basel, 1989. MR 997092, DOI 10.1007/978-3-0348-9152-3

1.

M. V. Keldysh, On the eigenvalues and eigenfunctions of certain classes of nonselfadjoint equations, Dokl. Akad. Nauk SSSR 77 (1951), 11-14.

2.

M. V. Keldysh, On completeness of the eigenfunctions of certain classes of nonselfadjoint linear operators, Uspehi Mat. Nauk 27 (1971), no. 4 (160), 15-41; English tranls. in Russian Math Surveys 27 (1971). MR 0300125

3.

I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Transl. Math. Monographs, vol. 18, Amer. Math. Soc., Providence, R.I., 1969. MR 246142

4.

M. G. Kreĭn and H. Langer, On the theory of quadratic pencils of selfadjoint operators, Dokl. Akad. Nauk SSSR 154 (1964), 1258-1261; English transl. in Soviet Math. Dokl. 5 (1964). MR 169060

5.

M. G. Kreĭn and H. Langer, On some mathematical principles in the linear theory of damped oscillations of continua, Applications of Function Theory in Continuum Mechanics (Proc. Internat. Sympos., Tbilisi, 1963), vol. 2, "Nauka", Moscow, 1965, pp. 283-322; English transl., Parts I, II, Integral equations operator theory 1 (1978), 364-399; 539-566. MR 511976

6.

L. Rodman, An introduction to operator polynomials, Operator Theory: Advances and Applications vol. 38, Birkhäuser Verlag, Basel, 1989. MR 997092