The theory of distributions originated in the work of Laurent Schwartz in the era 1945–1952 [Schl2]. Earlier work by Sobolev was along similar lines. The objective was to treat functions as functionals, and to notice that when so interpreted, differentiation was always possible. This opened the way to the study of partial differential equations by new methods that bypassed the classical restrictions on functions. The functionals that now become the focus of study are called “distributions”—not to be confused with distributions in probability theory! The term “generalized functions”is also used, especially by Russian authors.
KeywordsDifferential Operator Compact Support Fundamental Solution Null Space Heaviside Function
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