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

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Product of Hyperfunctions,tion, multiplication and division, the first two are, of course, possible as linear combinations. There are, however, problems with multiplication and division. It may even seem meaningless to consider products of hyperfunctions in a theory such as the Schwartz distribution theory which is based on

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Hilbert Transforms and Conjugate Hyperfunctions,t chapter is to treat them in a unified way from the viewpoint of hyperfunction theory. It will be seen that Hilbert transformation is just the same as convolution with the hyperfunction 1/. and the conjugate Fourier series is the Hilbert transform of a periodic hyperfunction (i.e. Fourier series).

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Poisson-Schwarz Integral Formulae,its normal derivative δФ/δn assumes specified values on the boundary. Many problems of physics and engineering can be reduced to this problem. In two-dimensional problems, an equivalent is to find an analytic function . regular in D such that Re . or Im . assumes specified values on the boundary. Wh

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Laplace Transforms,m is worked out for hyperfunctions, the theory will have much broader applicability than it has for ordinary functions. However, we need not deal with the Laplace transform .. We can deal with it as a variant representation of the Fourier transform in the framework of the theory of the Fourier trans

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Xiaoxu Li,Marcel Wira,Ruck Thawonmasd side represents ‘something’ determined by a pair of analytic functions: ..(.), F.-(.) , and write .. We call this ‘something‘ a .. To save space, it may be written [F.(.), F.(.)]. Alternatively, we may write the pair ..(.), .-(.) simply as .(.), so that (1.2) becomes: .(.)→.(.). (1.3)

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