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Double unconditional bases associated with a quadratic characteristic parameter problem
Authors:WM Greenlee
Institution:Department of Mathematics, University of Arizona, Tucson, Arizona 85721 USA
Abstract:A detailed discussion is given of the quadratic characteristic value problem, x = λPx + (1λ)Qx, where P and Q are compact selfadjoint operators in Hilbert space. Theorems are proven showing that unconditional bases of various types may be constructed from the root vectors of A(λ) = λP + (1λ)Q. These theorems are of interest in the stability theory of linear evolution equations, particularly for application to certain problems in the linearized theory of hydrodynamic stability.
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