Introduction to the Spectral Theory of Polynomial Operator Pencils

By A. Markus. 2012

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Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators (2012, background): “In relation with differential operators, these properties are discussed in the above-mentioned reviews, the book [57] and recent works [23], [1], [53], [73] and [27].”
Incomplete Inverse Spectral and Nodal Problems for Differential Pencils (2011, neutral): “For each ﬁxed x ∈ [0 , 1] the functions ϕ ( x, ρ ) , ψ ( x, ρ ) , S ( x, ρ ) together with their derivatives with respect to x are entire in ρ.”
NLEVP: A Collection of Nonlinear Eigenvalue Problems (2013, background): “R [Markus 1988, Section 34], are identi.ed by elliptic.”
An Instability Index Theory for Quadratic Pencils and Applications (2012, background): “Following Markus [30], generalized eigenfunctions are found by solving P2(0)a1 +P ′2(0)a0 = 0, a0 ∈ ker(A).”
Nonlinear Rayleigh functionals (2012, background): “This assumption is different and in some sense more restrictive than definiteness, respectively hyperbolicity, which assure real eigenvalues and have been established for the generalized eigenvalue problem [28], for the quadratic eigenvalue problem [29], and for polynomial problems of arbitrary degr”