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A Multiplying Factor Method for the Solution of Wiener-Hopf Equations†

Published online by Cambridge University Press:  20 January 2009

B. Noble  and
A. S. Peters
B. Noble
Affiliation:
The Royal College of Science and Technology, Glasgow
A. S. Peters
Affiliation:
The Institute of Mathematical Sciences, New York
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In (1), § 6.2, a multiplying factor method has been used to solve certain dual integral equations. The results are then used to solve a single integral equation of the Wiener-Hopf type. In this note we indicate how a related technique can be used to solve Wiener-Hopf integral equations directly. Consider

where

Define

where α = σ+iτ, and F+(α) is regular for τ>q; K(α) is regular and non-zero in −p < τ < p. For simplicity we restrict ourselves to the case where

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 12 , Issue 3 , June 1961 , pp. 119 - 122
Copyright
Copyright © Edinburgh Mathematical Society 1961

References

REFERENCE

(1)Noble, B., Methods based on the Wiener-Hopf technique for the solution of partial differential equations, Pergamon Press (1958).Google Scholar