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IV. A Modified Hilbert Transform

Published online by Cambridge University Press:  14 February 2012

D. S. Jones
D. S. Jones
Affiliation:
Department of Mathematics, University of Dundee
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Summary

The solution of certain integral equations, which are related to the Hilbert transform, is discussed from the viewpoint of generalized functions. The behaviour of the corresponding transforms in the complex plane is examined for generalized functions which effectively vanish at infinity. A space of generalized functions which need not be small at infinity is introduced and the integral equations solved in this space. Various possible extensions of the theory are also mentioned.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 69 , Issue 1 , 1970 , pp. 45 - 76
Copyright
Copyright © Royal Society of Edinburgh 1970

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References

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