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The Spectral resolution of Watson transforms†

Published online by Cambridge University Press:  24 October 2008

Edwin J. Akutowicz
Edwin J. Akutowicz
Affiliation:
Massachusetts Institute of Technology
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Extract

If φ belongs to L2(0, ∞), the Watson transform W φ of φ is defined by

where k(u)/u belongs to L2(0, ∞) and

The operator W is unitary in L2(0, ∞), and its inverse is given by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 3 , July 1958 , pp. 368 - 376
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

REFERENCES

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