2010 | OriginalPaper | Buchkapitel
Introduction to Hyperfunctions
verfasst von : Urs Graf
Erschienen in: Introduction to Hyperfunctions and Their Integral Transforms
Verlag: Birkhäuser Basel
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After a short overview of generalized functions and of the different ways they can be defined, the concept of a hyperfunction is established, followed by an introduction to the most simple and familiar hyperfunctions. Then the elementary operational properties of hyperfunctions are presented. The so-called finite part hyperfunctions are introduced, followed by the important notion of the (definite) integral of a hyperfunction. The chapter closes with a definition of more familiar hyperfunctions frequently used in applications. The books of [19, Imai] and [20, Kaneko] are the principal references for this chapter.