## Distributions: An OutlineIn a simple but mathematically coherent manner, this text examines the basis of the distribution theories devised by Schwartz and by Mikusinki. Rigorous and concise, it surveys the functional theory of distributions as well as the algebraic theory. Its easy generalizations offer applications to a wide variety of problems. The two-part treatment begins with the functional theory of distributions, exploring differentiation, formation of products, translation and regularization, convergence, Fourier transforms, and partial differential equations. The second half focuses on the algebraic theory of distributions, with discussions of derivatives and integrals, differential and integral equations, relations to the Laplace transform, convergence, translation and the exponential function, and partial differential equations. Geared to students of mathematics, this text will also prove instructive to physicists and applied scientists. |

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algebraic algebraisation analysis application bution calculation commutative law commutative ring compact support complex numbers composition product condition constant coefﬁcients continuous functions continuous operation corresponds DEFINITIONI denoted dense in 9 density derivatives differentiation and integration Dirac measure direct product distri distribution theory divisor of zero element a e example exists exponential function fact ﬁnally ﬁnd ﬁnite number ﬁrst ﬁxed compact formula Fourier theory Fourier transform functions f generalised functions give Heaviside function indeﬁnitely differentiable functions inﬁnity integrable functions integral equations introduce inverse inverse element Laplace transform let us consider limit linear and continuous linear differential equations linear functional linear space multiplication product neutral element notation pairs partial differential equations possible postulate problem proof rational numbers ring without divisor satisﬁed Schwartz simplicity solution space 9 subset temperate distribution theorem theory of distributions tion transforms 9 translation unique unit element usual sense