1. Basic concept
The concept of a distribution, originally known as a generalized function, is a relatively recent but fundamental concept in physics. This tool, introduced empirically by Dirac at the beginning of the century, was given a rigorous mathematical formulation in the years 1945–1950, largely thanks to the work of Laurent Schwartz. Among distributions, the Dirac delta function, now called the Dirac distribution, plays a key role.
The delta function was introduced as the limit, as ε → 0 + , of functions (or functions of the same type) (Figure 1 ):
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