Opuscula Math. 33, no. 2 (2013), 307-321
http://dx.doi.org/10.7494/OpMath.2013.33.2.307

 
Opuscula Mathematica

Variational characterizations for eigenfunctions of analytic self-adjoint operator functions

Georgios Katsouleas
John Maroulas

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.

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  • Georgios Katsouleas
  • National Technical University of Athens, Dept. of Mathematics, Zografou Campus, Athens 15780, Greece
  • John Maroulas
  • National Technical University of Athens, Dept. of Mathematics, Zografou Campus, Athens 15780, Greece
  • Received: 2012-03-20.
  • Revised: 2012-08-01.
  • Accepted: 2012-10-25.
Opuscula Mathematica - cover

Cite this article as:
Georgios Katsouleas, John Maroulas, Variational characterizations for eigenfunctions of analytic self-adjoint operator functions, Opuscula Math. 33, no. 2 (2013), 307-321, http://dx.doi.org/10.7494/OpMath.2013.33.2.307

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