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Basic Terminology, Notation and Conventions

We begin our review of the mathematical preliminaries by discussing how we will describe some of the basic entities of Fourier analysis—numbers, functions and operators. Perhaps the most important part of this discussion is in determining just what will be meant by the phrase “f is a function” and by the notation “f (x)”. Pay close attention to this discussion even if you think you know what a “function” is. It turns out that people in different disciplines have developed slightly different views as to the meaning of this word. That is one reason a text on Fourier analysis by a mathematician specializing in functional analysis will often look quite different from a corresponding text by an electrical ...

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