Distributions Defined by Divergent Integrals

Ram P. Kanwal
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Ram P. Kanwal: The Pennsylvania State University, Department of Mathematics

Chapter Chapter 4 in Generalized Functions, 2004, pp 71-98 from Springer

Abstract: 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.

Keywords: Integrable Function; Delta Function; Analytic Continuation; Simple Polis; Homogeneous Function (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-8176-8174-6_4

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