Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T07:42:51.812Z Has data issue: false hasContentIssue false

Spectral representations for families of self-adjoint operators

Published online by Cambridge University Press:  24 October 2008

Michael M. Broido
Affiliation:
Trinity College, Cambridge†

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
Copyright
Copyright © Cambridge Philosophical Society 1966

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Jauch, J. M. and Misra, B.The spectral representation. Helv. Phys. Acta, 38 (1965), 3052.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), 349352.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