# Schwartz, Laurent

### function delta definition mathematical

(1915– ) French mathematician.

Schwartz was educated at the École Normale Supérieure and the Faculty of Science in Paris. Later he became a professor at Nancy. He was awarded the Fields Medal for mathematics in 1950 for major contributions to functional analysis. Increasingly, mathematical physicists had needed to use the Dirac delta function d(x) to perform calculations with properties such as mass, energy, impulse, etc., concentrated at a single point or instant when x = 0. The delta function was treated as zero, unless x = 0 when it was infinite; however the area under the curve or integral was taken to be unity. The problem was that this definition was insufficient to make d(x) a function in the strict sense, and it could not be manipulated mathematically. Schwartz successfully offered a generalized definition, which was a rigorous function. Following this the delta function has become a crucial element of many important areas of mathematical physics such as potential theory, partial differential equations and Green’s functions.

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