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An application of distribution theory to Martin's method in potential scattering

Published online by Cambridge University Press:  24 October 2008

A. T. Whipp
A. T. Whipp
Affiliation:
Department of Theoretical Physics, University of Liverpool, Liverpool, England
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Abstract

In order to study the convergence of a series arising from the use of Martin's method in potential scattering a framework consisting of a modifidation to Schwartz's formulation of distribution theory is set up. This modification makes essential use of norms on the spaces of test functions and linear functionals. By making the norm on the space of test functions satisfy extra axioms a bound is obtained on the norm of a generalized convolution of two linear functionals, and this bound is used to prove the convergence of the series. The proof of convergence is generalized to cover the multi-channel problem. The method used may also be applied to many other physical problems.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 3 , November 1970 , pp. 709 - 718
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Mabtin, A.Progr. Elem. Ptcl. Phys. 7 (1966), 1–66.Google Scholar
(2) See for example, Marchand, J.Distributions (North-Holland Publishing Co., 1962), chapter 1.Google Scholar
(3)Dieudonné, J.Foundations of modern analysis (Academic Press Inc.; New York, 1960), chapters 5–9.Google Scholar