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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An Impossible Yet Necessary Task(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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Learning and Using Specific Instances,established tauberian theorems for Fourier-Laplace transforms of generalized functions in the complex domain. In the present work Pseudo-asymptotic expansion (p.a.e.) of generalized functions is defined as an improvement over its quasi-asymptotic expansion (q.a.e.) providing an error term in q.a.e.

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,Generalized D’Alembert Functional Equation in Distributions,fining certain operators on Schwartz distributions and using these to reformulate the classical equation. It is shown that for regular distributions (i.e. locally integrable functions), the distributional solution reduces to the classical one.

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