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

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Fourier Transformation of Power-Type Hyperfunctions, as ordinary functions. However, as will be seen later, these power-type hyperfunctions play decisive roles when we investigate the asymptotic behaviour of the Fourier transforms .(ξ) = ..(.) for ξ → ∞ for a given function . (.).

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Poisson-Schwarz Integral Formulae,en D is a circle or a halfplane, formulae to express the solution are known and are called the .. In this chapter, we discuss these formulae and related facts from the viewpoint of hyperfunction theory. As an example of their application we deal with integral equations related to the Hilbert transforms.

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Miriam-Linnea Hale,André Melzert . = O. Therefore, ..(.) and ..(.) are simpler than .(.) itself, so that it may be convenient to consider hyperfunctions corresponding to .. (.) and ..(.) and to combine them to obtain the hyperfunction corresponding to .(.).

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Periodic Hyperfunctions and Fourier Series Fourier Series,his chapter we study periodic hyperfunctions. Then we shall see that the theory of Fourier series is naturally absorbed into the theory of Fourier transformations. For this purpose, we shall first introduce the concept of standard generating functions.