Spectral Theory of Self-Adjoint Operators

The present chapter is devoted to the introduction of the notation, the definitions and most of the results from functional analysis which will be needed in the sequel. Because of lack of space, we refrain from explaining the motivations behind the numerous definitions we introduce. We merely illustrate them with examples of Schrodinger operators and we postpone a more detailed study to Chapter II. Rather than a serious introduction to the spectral theory of self-adjoint operators, this chapter should be understood as a glossary and a summary of the terms and results to be used in the sequel.