Titlebook: Applied Hyperfunction Theory; Isao Imai Book 1992 Springer Science+Business Media Dordrecht 1992 Fourier series.analytic function.differen

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Integral Equations, were taken up as examples. Since the aim was to show applications of Hilbert transforms, we considered only integral equations of very special types. In this chapter, we choose examples of integral equations from a wider domain and explain how to deal with them using hyperfunction theory.

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Mathematics and its Applicationshttp://image.papertrans.cn/a/image/159862.jpg

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Thorsten Hennig-Thurau,Mark B. HoustonLet us begin with two ordinary functions ..(.) and ..(.) and suppose that their Fourier transforms . exist. The Fourier transform of the product ..(.) · ..(.) is . Since ..(.) is the inverse Fourier transform of ψ(ξ), we have . Substituting this into the r.h.s. of (1.2) gives..

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