| 期刊全稱 | Applied Hyperfunction Theory | | 影響因子2023 | Isao Imai | | 視頻video | http://file.papertrans.cn/160/159862/159862.mp4 | | 學(xué)科分類 | Mathematics and its Applications | | 圖書(shū)封面 |  | | 影響因子 | Generalized functions are now widely recognized as importantmathematical tools for engineers and physicists. But they areconsidered to be inaccessible for non-specialists. To remedy thissituation, this book gives an intelligible exposition of generalizedfunctions based on Sato‘s hyperfunction, which is essentially the`boundary value of analytic functions‘. An intuitive image --hyperfunction = vortex layer -- is adopted, and only an elementaryknowledge of complex function theory is assumed. The treatment isentirely self-contained. .The first part of the book gives a detailed account of fundamentaloperations such as the four arithmetical operations applicable tohyperfunctions, namely differentiation, integration, and convolution,as well as Fourier transform. Fourier series are seen to be nothingbut periodic hyperfunctions. In the second part, based on the generaltheory, the Hilbert transform and Poisson-Schwarz integral formula aretreated and their application to integral equations is studied. Agreat number of formulas obtained in the course of treatment aresummarized as tables in the appendix. In particular, those concerningconvolution, the Hilbert transform and Fourier transform co | | Pindex | Book 1992 |
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