Article | REF: AF568 V1

The spectral theorem

Author: Marc LENOIR

Publication date: October 10, 2012

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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

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