A quadratic eigenvalue problem
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- by W. M. Greenlee PDF
- Proc. Amer. Math. Soc. 40 (1973), 123-127 Request permission
Abstract:
Let $P,Q$ be compact selfadjoint operators in a Hilbert space. It is proven that the characteristic and associated vectors of the quadratic eigenvalue problem, $x = \lambda Px + (1/\lambda )Qx$, form a Riesz basis for the cartesian product of the closure of the range of $P$ and the closure of the range of $Q$.References
- Dž. È. Allahverdiev, Multiply complete systems and nonselfadjoint operators depending upon a parameter $\lambda$, Dokl. Akad. Nauk SSSR 166 (1966), 11–14 (Russian). MR 0199513
- N. K. Askerov, S. G. Kreĭn, and G. I. Laptev, The problem of the oscillations of a viscous liquid and the operator equations connected with it, Funkcional. Anal. i Priložen. 2 (1968), no. 2, 21–31 (Russian). MR 0232233
- S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, International Series of Monographs on Physics, Clarendon Press, Oxford, 1961. MR 0128226
- Avner Friedman and Marvin Shinbrot, Nonlinear eigenvalue problems, Acta Math. 121 (1968), 77–125. MR 250096, DOI 10.1007/BF02391910
- 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
- I. S. Iohvidov, On the spectra of Hermitian and unitary operators in a space with indefinite metric, Doklady Akad. Nauk SSSR (N.S.) 71 (1950), 225–228 (Russian). MR 0035923
- I. S. Iohvidov and M. G. Kreĭn, Spectral theory of operators in spaces with indefinite metric. I, Amer. Math. Soc. Transl. (2) 13 (1960), 105–175. MR 0113145
- S. G. Kreĭn and G. I. Laptev, On the problem of the motion of a viscous fluid in an open vessel, Funkcional. Anal. i Priložen. 2 (1968), no. 1, 40–50 (Russian). MR 0248462
- A. I. Mal′cev, Osnovy Lineĭnoĭ Algebry, OGIZ, Moscow-Leningrad, 1948 (Russian). MR 0033268
- R. E. L. Turner, A problem in Rayleigh-Taylor instability, Rend. Sem. Mat. Univ. Padova 42 (1969), 305–323. MR 261184
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 123-127
- MSC: Primary 47A70
- DOI: https://doi.org/10.1090/S0002-9939-1973-0328648-7
- MathSciNet review: 0328648