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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

(1)Doetsch, G.Die Eigenwerte und Eigenfunktionen von Integral-transformationen. Math. Ann. 117 (1939).Google Scholar
(2)Pollard, H.Integral transforms. Duke Math. J. 13 (1946).CrossRefGoogle Scholar
(3)Plessner, A. and Rokhlin, V.Spectral theory of linear operators. Uspehi Mat. Nauk, 1 (N.S.), 1946.Google Scholar
(4)Murray, F. J.Linear transformations in Hilbert Space (Princeton, 1941).Google Scholar
(5)Nagy, Béla v. Sz.Spektraldarstellung Linearer Transformationen des Hilbertschen Raumes (Berlin, 1942).CrossRefGoogle Scholar
(6)Nevastlinna, F. and Nieminen, T.Das Poisson-Stieltjessche Integral und seine Anwendung in der Spektraltheorie des Hilbertschen Raumes. Ann. Acad. Sci. Fenn. No. 207 (1955).Google Scholar