Distributions Defined by Divergent Integrals

  • Ram P. Kanwal


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.


Integrable Function Delta Function Analytic Continuation Simple Polis Homogeneous Function 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Ram P. Kanwal
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA

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