Opuscula Math. 33, no. 2 (2013), 307-321
Variational characterizations for eigenfunctions of analytic self-adjoint operator functions
Abstract. In this paper we consider Rellich's diagonalization theorem for analytic self-adjoint operator functions and investigate variational principles for their eigenfunctions and interlacing statements. As an application, we present a characterization for the eigenvalues of hyperbolic operator polynomials.
Keywords: operator functions, eigenfunctions, eigenvalues, variational principles.
Mathematics Subject Classification: 15A22, 15A18, 47A56, 47A75, 49R50.
- Received: 2012-03-20.
- Revised: 2012-08-01.
- Accepted: 2012-10-25.