Variational characterizations for eigenfunctions of analytic self-adjoint operator functions (Q2871597)

The authors deal with a variational theory for analytic functions \(P(\lambda)\) whose values are self-adjoint operators acting on a finite dimensional Hilbert space, with \(\lambda\in\mathbb{R}\). Using a Rellich theorem (see the book by \textit{I. Gohberg} et al.\ [Matrix polynomials. New York etc.: Academic Press (1982; Zbl 0482.15001)]), applied to diagonalize the function \(P(\lambda)\), the authors give a variational characterization of the corresponding eigenvalues. In particular, they characterize the eigenvalues of hyperbolic operator polynomials.