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Spectral representations for families of self-adjoint operators

Published online by Cambridge University Press:  24 October 2008

Michael M. Broido
Michael M. Broido
Affiliation:
Trinity College, Cambridge†
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Abstract

Spectral theorems and a functional calculus for families of permutable self-adjoint operators in a separable Hilbert space are developed in a form convenient for physical applications. A recent paper of Jauch and Misra is discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 2 , April 1966 , pp. 209 - 213
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Jauch, J. M. and Misra, B.The spectral representation. Helv. Phys. Acta, 38 (1965), 30–52.Google Scholar
(2)Michael, E. A.Locally multiplieatively-convex topological algebras. Mem. Amer. Math. Soc. no. 11 (1952).Google Scholar
(3)Gelfand, I. M. and Kostiuchenko, A. G.On the eigenfunction expansions of differential and other operators, Dokl. Akad. Nauk SSSR, 103 (1955), 349–352.Google Scholar
(4)Gelfand, I. M. and Vilenkin, N. Ja.Generalized functions, vol. 4 (Fizmatigiz, Moscow 1961).Google Scholar
(5)Broido, M. M.On the equations of quantum field theory. Churchill College, Cambridge, Fellow-ship dissertation, 02 1965.Google Scholar
(6)Riesz, F. and Sz.-Nagy, B.Leçons d'anolyse fonctionelle e.g. (in English) Blackie.Google Scholar
(7)Dixmier, J.Les algèbres d'opérateurs dans l'espace hilbertien (Gauthier-Villars, 1957).Google Scholar