A non standard approach of spectral theory of self-adjoint operators (generalized Gelfand eigenvectors)

Abstract

Let $u={\int }_{-\infty }^{+\infty }\lambda d{E}_{\lambda }$ 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.

12 pages