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Generalized functions are now widely recognized as important
mathematical tools for engineers and physicists. But they are
considered to be inaccessible for non-specialists. To remedy this
situation, this book gives an intelligible exposition of
generalized functions 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 elementary knowledge of complex function theory is assumed.
The treatment is entirely self-contained. The first part of the
book gives a detailed account of fundamental operations such as the
four arithmetical operations applicable to hyperfunctions, namely
differentiation, integration, and convolution, as well as Fourier
transform. Fourier series are seen to be nothing but periodic
hyperfunctions. In the second part, based on the general theory,
the Hilbert transform and Poisson-Schwarz integral formula are
treated and their application to integral equations is studied. A
great number of formulas obtained in the course of treatment are
summarized as tables in the appendix. In particular, those
concerning convolution, the Hilbert transform and Fourier transform
contain much new material. For mathematicians, mathematical
physicists and engineers whose work involves generalized functions.
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