Fourier Transforms

Urs Graf ()

Chapter Chapter 4 in Introduction to Hyperfunctions and Their Integral Transforms, 2010, pp 241-274 from Springer

Abstract: Abstract From the outset we shall explore the relation between Laplace and Fourier transforms. The subclass of hyperfunctions of slow growth S( ℝ) and their Fourier transforms are introduced. It will be shown that the Fourier transform of a hyperfunction can be computed by evaluating the Laplace transform of two rightsided hyperfunctions. This fact is exploited to the hilt in the sequel, almost all Fourier transforms in this book are computed via Laplace transforms. The inverse Fourier transformation and the important Reciprocity Rule are formulated for hyperfunctions. All operational rules for the Fourier transform of hyperfunctions are carefully established. Conditions for the validity of the convolution property of Fourier transformation are stated. Many concrete examples of Fourier transforms of hyperfunctions are presented. The chapter terminates with Poisson’s summation formula and some applications to differential and integral equations.

Keywords: Fourier Transform; Slow Growth; Real Axis; Operational Property; Inverse Fourier Transform (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_4

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

DOI: 10.1007/978-3-0346-0408-6_4

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 ().