A non standard approach of spectral theory of self-adjoint operators   (generalized Gelfand eigenvectors)
  Let $u=\int_{-\infty}^{+\infty}\lambda dE_{\lambda}$ be a self-adjoint operator in a Hilbert space $H$. Our purpose is to provide a non-standard description of the spectral family $(E_{\lambda})$ and the generalized Gelfand eigenvectors. 
Fatma Karray Meziou