Abstract
In the previous chapters we have defined various singular distributions. One of them is Pf(l/x), defined in Example 4 of Section 2.4. The function 1/x is not integrable on any neighborhood of the origin. We succeeded in regularizing this function by defining the functionalPf (l/x) by the principal value of the singular integral defined by the quantity (φ, 1/x). The aim of this chapter is to extend this idea and to regularize various singular integrals and thereby define the coresponding distributions. Let us start with a simple example.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kanwal, R.P. (2004). Distributions Defined by Divergent Integrals. In: Generalized Functions. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8174-6_4
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8174-6_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4343-0
Online ISBN: 978-0-8176-8174-6
eBook Packages: Springer Book Archive