On extended eigenvalues and extended eigenvectors of some operator classes

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.