Work
Sobolev introduced the notions that are now fundamental for several areas of mathematics. Sobolev spaces can be defined by some growth conditions on the Fourier transforms; they and their embedding theorems are an important subject in functional analysis. Generalized functions (later known as distributions) were first introduced by Sobolev in 1935 for weak solutions, and further developed by Laurent Schwartz. Sobolev abstracted the classical notion of differentiation so expanding the ranges of applications of the technique of Newton and Leibniz. The theory of distribution is considered now as the calculus of the modern epoch.
Read more about this topic: Sergei Sobolev
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