Fold completeness of a system of root vectors of a system of unbounded polynomial operator pencils in Banach spaces. I. Abstract theory

Yakov Yakubov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

N. Dunford and J.T. Schwartz (1963) striking Hilbert space theory about completeness of a system of root vectors (generalized eigenvectors) of an unbounded operator has been generalized by J. Burgoyne (1995) to the Banach spaces framework. We use the Burgoyne's theorem and prove n-fold completeness of a system of root vectors of a system of unbounded polynomial operator pencils in Banach spaces. The theory will allow to consider, in application, boundary value problems for ODEs and elliptic PDEs which polynomially depend on the spectral parameter in both the equation and the boundary conditions.

Original languageEnglish
Pages (from-to)263-275
Number of pages13
JournalJournal des Mathematiques Pures et Appliquees
Volume92
Issue number3
DOIs
StatePublished - Sep 2009

Keywords

  • Approximation numbers
  • Discrete spectrum
  • Fold completeness
  • Gelfand numbers

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