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Introduction to Hyperfunctions

In: Introduction to Hyperfunctions and Their Integral Transforms

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  • Urs Graf

Abstract

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.

Suggested Citation

  • Urs Graf, 2010. "Introduction to Hyperfunctions," Springer Books, in: Introduction to Hyperfunctions and Their Integral Transforms, chapter 0, pages 1-62, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0346-0408-6_1
    DOI: 10.1007/978-3-0346-0408-6_1
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