On extended eigenvalues and extended eigenvectors of some operator classes

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Karaev M.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.134, no.8, pp.2383-2392, 2006 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 134 Issue: 8
  • Publication Date: 2006
  • Doi Number: 10.1090/s0002-9939-06-08258-x
  • Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.2383-2392

Abstract

We give a complete description of the set of extended eigenvectors of the Volterra integration operator V, Vf(x) = integral(x)(0) f(t)dt, on L-2 [0,1], which strengthens the result of a paper by Biswas, Lambert, and Petrovic (2002). We also introduce the concept of a well splitting operator and study its extended eigenvalues and extended eigenvectors.