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- W132686583 abstract "Hilbert transforms and conjugate Fourier series are often used in the solution of problems of physical sciences and engineering. The aim of the present 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/x and the conjugate Fourier series is the Hilbert transform of a periodic hyperfunction (i.e. Fourier series). Therefore, the content of this chapter can be regarded as an application of Chapters 13 and 14. Since the Poisson-Schwarz integration formula of complex function theory will be discussed from the viewpoint of hyperfunction theory, we also derive several formulae on which the Poisson-Schwarz formula is based." @default.
- W132686583 created "2016-06-24" @default.
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- W132686583 date "1992-01-01" @default.
- W132686583 modified "2023-09-27" @default.
- W132686583 title "Hilbert Transforms and Conjugate Hyperfunctions" @default.
- W132686583 doi "https://doi.org/10.1007/978-94-011-2548-2_15" @default.
- W132686583 hasPublicationYear "1992" @default.
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