Introduction to Hyperfunctions and Their Integral Transforms
An Applied and Computational Approach
2010, Approx. 430 p.
A product of Birkhäuser Basel
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Offers an introduction to the subject of generalized functions and their integral transforms by an approach based on the theory of functions of one complex variable
Readable by a large audience due to the use of basic contour integration in the complex plane
Only book that treats Mellin and Hankel transforms
This textbook presents an elementary introduction to generalized functions by using Sato's approach of hyperfunctions which is based on complex function theory. This very intuitive and appealing approach has particularly great computational power.
The concept of hyperfunctions and their analytic properties is introduced and discussed in detail in the first two chapters of the book. Thereafter the focus lies on generalizing the (classical) Laplace, Fourier, Hilbert, Mellin, and Hankel transformations to hyperfunctions. Applications to integral and differential equations and a rich variety of concrete examples accompany the text throughout the book.
Requiring only standard knowledge of the theory of complex variables, the material is easily accessible for advanced undergraduate or graduate students. It serves as well as a reference for researchers in pure and applied mathematics, engineering and physics.