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Laurent-Moïse Schwartz (French: [lɔʁɑ̃ mɔiz ʃvaʁts]; 5 March 1915 – 4 July 2002) was a French mathematician.He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function.
An influential book on operational calculus was Oliver Heaviside's Electromagnetic Theory of 1899. When the Lebesgue integral was introduced, there was for the first time a notion of generalized function central to mathematics. An integrable function, in Lebesgue's theory, is equivalent to any other which is the same almost everywhere. That ...
In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz (Schwartz distributions) have a two-variable theory that includes all reasonable bilinear forms on the space of test functions.
In algebra and number theory, a distribution is a function on a system of finite sets into an abelian group which is analogous to an integral: it is thus the algebraic analogue of a distribution in the sense of generalised function. The original examples of distributions occur, unnamed, as functions φ on Q/Z satisfying [1]
Gårding (1997) comments that although the ideas in the transformative book by Schwartz (1951) were not entirely new, it was Schwartz's broad attack and conviction that distributions would be useful almost everywhere in analysis that made the difference. A detailed history of the theory of distributions was given by Lützen (1982).
[3] This theory, known as the Kunita-Watanabe extension is based on the crucial Kunita–Watanabe inequality for the stochastic integral. [ 4 ] Another important contribution of Watanabe has been to use the Malliavin calculus to establish a theory of generalized functionals on Wiener space , by analogy to Laurent Schwartz 's theory of ...
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Prof Sergei Lvovich Sobolev, FRSE (Russian: Серге́й Льво́вич Со́болев; 6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations. Sobolev introduced notions that are now fundamental for several areas of mathematics.
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