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1. Introduction
The spectral theorem, notwithstanding its abstract aspect, is the foundation or model on which many applications are based, whether of a theoretical nature such as the study of operator algebras, or of a more practical nature such as that of partial differential equations.
1.1 Two examples
There's nothing extraordinary about the situation described in the preamble, but let's take a look at two examples in the context of sequences or functions with integrable squares.
In the space of summable square sequences, it is easy to construct an operator, let D be,...
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PAULIN (F.). – Complements to spectral theory and harmonic analysis http://www.math.u-psud.fr/∼ paulin/notescours/cours_magistere2.pdf
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