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On Gordon's method of solving dual integral equations

Published online by Cambridge University Press:  18 May 2009

J. Burlak
J. Burlak
Affiliation:
North Carolina State College Raleigh, North Carolina, U.S.A.
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1. Dual integral equations of the form

where f(x) and g(x) are given and Ψ(x) is the unknown, have been increasingly studied in recent years; the first solutions were given for the case g(x) ≡ 0 by Titchmarsh [1] (for 0 < α < 2) and Busbridge [2] (for — 2 < α < 0). An interesting and much simpler method of solving the equations in the same case, g ≡ 0, was given by Gordon [3]. He also showed that the problem of solving the general equations (1) and (2) can be reduced to a problem in which g ≡ 0. He did not pursue this idea as far as finding and simplifying the solution of (1) and (2) but this has been done recently (see [4]) and Noble [5] used a similar idea in treating the case f ≡ 0.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 3 , January 1964 , pp. 117 - 122
Copyright
Copyright © Glasgow Mathematical Journal Trust 1964

References

REFERENCES

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