This operator does not have any eigenvectors in , though it does have eigenvectors in a larger space. Namely the distribution , where is the Dirac delta function, is an eigenvector when construed in an appropriate sense. The Dirac delta function is however not a function in the classical sense and does not lie in the Hilbert space or any other Banach space. Thus, the delta-functions are "generalized eigenvectors" of but not eigenvectors in the usual sense.
This operator does not have any eigenvectors in , though it does have eigenvectors, in a larger space. Namely the distribution  where is the Dirac delta. function is an eigenvector when construed in an appropriate sense The Dirac delta function is however not a function in the classical sense and does not lie in the Hilbert space or any other Banach space. T,hus, the delta-functions are "generalized eigenvectors" of but not eigenvectors in the usual sense.