Stone’s theorem for a group of unitary operators over a Hilbert space
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- by Habib Salehi PDF
- Proc. Amer. Math. Soc. 31 (1972), 480-484 Request permission
Abstract:
The spectral representation for a group of unitary operators acting on a Hilbert space where the parameter set is a separable real Hilbert space is obtained. The usual spectral representation of such a group of unitary operators is when the parameter set is a locally compact abelian group (Stone’s theorem). The main result used in the proof is the Bochner theorem on the representation of positive definite functions on a real Hilbert space.References
- Warren Ambrose, Spectral resolution of groups of unitary operators, Duke Math. J. 11 (1944), 589–595. MR 11172
- Leonard Gross, Harmonic analysis on Hilbert space, Mem. Amer. Math. Soc. 46 (1963), ii+62. MR 161095
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- Milton Rosenberg, Mutual subordination of multivariate stationary processes over any locally compact abelian group, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 12 (1969), 333–343. MR 251790, DOI 10.1007/BF00538754
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 480-484
- MSC: Primary 47A60; Secondary 46G99
- DOI: https://doi.org/10.1090/S0002-9939-1972-0300128-3
- MathSciNet review: 0300128