Laplace Transforms

Urs Graf ()

Chapter Chapter 3 in Introduction to Hyperfunctions and Their Integral Transforms, 2010, pp 155-239 from Springer

Abstract: Abstract We assume that the reader will have some degree of familiarity with the subject of classical Laplace transformation such as presented for example in [14, Graf]. After a discussion on loop integrals of Hankel type and their ramifications, some facts about the classical two-sided Laplace transformation are recalled. Then, the two subclasses of hyperfunctions, the right-sided and left-sided originals and their Laplace transforms, are defined by using loop integrals. The Laplace transform of a hyperfunction with an arbitrary support is handled by decomposing it into a sum of a left-sided and right-sided original (canonical splitting); it is then shown that its practical computation can be reduced to the evaluation of two right-sided Laplace transforms. Many concrete examples of Laplace transforms of hyperfunctions are presented. The operational rules of Laplace transforms of hyperfunctions are clearly stated. The subject of inverse Laplace transforms and convolutions follows. Fractional integrals and derivatives of right-sided hyperfunctions are briefly over-viewed. The application track with Volterra integral equations and convolution integral equations over an infinite range concludes the chapter. This chapter represents the core of the integral transformations part of the book. The following chapters on Fourier and Mellin transformations are heavily based on the results of this chapter. Another similar approach, due to Komatsu introducing the so-called Laplace hyperfunctions, is sketched in the Appendix.

Keywords: Entire Function; Image Function; Laplace Transform; Volterra Integral Equation; Vertical Strip (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0346-0408-6_3

Ordering information: This item can be ordered from
http://www.springer.com/9783034604086

DOI: 10.1007/978-3-0346-0408-6_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().