On extended eigenvalues and extended eigenvectors of some operator classes

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.