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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On extended eigenvalues and extended eigenvectors of some operator classes


Author: M. T. Karaev
Journal: Proc. Amer. Math. Soc. 134 (2006), 2383-2392
MSC (2000): Primary 47A15
Published electronically: March 21, 2006
MathSciNet review: 2213712
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Abstract: We give a complete description of the set of extended eigenvectors of the Volterra integration operator $ V,$ $ Vf(x)=\underset{0}{\overset{x}{\int }} f(t)dt$, on $ L^{2}\left[ 0,1\right] $, 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.


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Additional Information

M. T. Karaev
Affiliation: Department of Mathematics, Suleyman Demirel University, 32260 Isparta, Turkey
Email: garayev@fef.sdu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08258-X
PII: S 0002-9939(06)08258-X
Keywords: Extended eigenvalue, extended eigenvector, Volterra integration operator
Received by editor(s): March 3, 2005
Received by editor(s) in revised form: March 14, 2005
Published electronically: March 21, 2006
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society