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Titlebook: Generalized Functions and Their Applications; R. S. Pathak Book 1993 Springer Science+Business Media New York 1993 Manifold.Standard.diffe

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书目名称Generalized Functions and Their Applications
编辑R. S. Pathak
视频video
图书封面Titlebook: Generalized Functions and Their Applications;  R. S. Pathak Book 1993 Springer Science+Business Media New York 1993 Manifold.Standard.diffe
描述The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat‘s work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathemati
出版日期Book 1993
关键词Manifold; Standard; differential equation; equation; function; geometry; linear optimization; mathematics; m
版次1
doihttps://doi.org/10.1007/978-1-4899-1591-7
isbn_softcover978-1-4899-1593-1
isbn_ebook978-1-4899-1591-7
copyrightSpringer Science+Business Media New York 1993
The information of publication is updating

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Applications of Generalized Functions to Shocks and Discrete Models,tion. Generalized functions are also a powerful tool to formulate in a unified manner fundamental physical laws. We shall give here two general examples of such an application of generalized functions. The first is to the writing of the equations satisfied by shock waves : we establish in particular
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Nonstandard Treatments of New Generalised Functions,lombeau and others. The new generalised functions of Colombeau [1], [2], [3], [4], include distributions as a special sub-class, together with various non-linear functions of them. In particular the multiplication problem is comprehensively solved and expressions such as δ., δ. and so on are meaning
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Interplay between Singularities Asymptotics and Generalized Functions,.We start with the basic concepts of the sifting property of the delta function and the fact that it is the derivative of the Heaviside function. Then we build up the derivatives of the generalized functions across a surface of discontinuity. We demonstrate that this information is sufficient to der
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Hyperfunctions, Ultradistributions and Microfunctions,(Ω) in 1948–51. Dirac’s . function and Hadamard’s finite part of .., . < -1, are famous. More generally P. Lévy [16] had determined the dual of ..([a, b]). Yet the true history of generalized functions started with Schwartz.
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