Extended eigenvalues and the Volterra operator

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https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/extended-eigenvalues-and-the-volterra-operator/15E05076D3849E20B3F1CF5FB58E95D1

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https://doi.org/10.1017/S001708950203015X
 http://hdl.handle.net/11603/36953

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UMBC Mathematics and Statistics Department

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https://orcid.org/0000-0001-8594-0568

Date

2003-02-26

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journal articles
preprints
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Biswas, Animikh, Alan Lambert, and Srdjan Petrovic. “Extended Eigenvalues and the Volterra Operator.” Glasgow Mathematical Journal 44, no. 3 (September 2002): 521–34. https://doi.org/10.1017/S001708950203015X.

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@2002 Glasgow Mathematical Journal Trust. This work has been accepted for publication.

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Abstract

In this paper we consider the integral Volterra operator on the space L²(0,1). We say that a complex number λ is an extended eigenvalue of V if there exists a nonzero operator X satisfying the equation XV=λVX. We show that the set of extended eigenvalues of V is precisely the interval (0, ∞) and the corresponding eigenvectors may be chosen to be integral operators as well.