Titlebook: Mathematical Methods in Physics; Distributions, Hilbe Philippe Blanchard,Erwin Brüning Textbook 2015Latest edition Springer International P

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Calculus for Distributionsugh the duality method. First differentiation is introduced and it turns out that all distributions are infinitely often differentiable. Next multiplication of distributions with . functions is defined and it follows that the product rule of differentiation holds. Tempered distributions can only be

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Convolution Productsnd study the differentiability and integrability properties of the convolution product. It turns out that the test function space of strongly decreasing . function . is a commutative algebra when equipped with the convolution product. Then the convolution of a distribution with a test function is in

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Fourier Transformationmation a powerful tool of analysis, in particular in the solution theory for constant coefficient partial differential operators .(.). The proof of this result is prepared by establishing that the Fourier transformation is an isomorphism of the topological vector space .. We determine the image of v

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