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

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

2006-11-09

arxiv.org/abs/math/0611277v1

Mathematics

Functional Analysis

12 pages

Scientific paper

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.

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