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Acta Applicandae Mathematica

, Volume 6, Issue 1, pp 19–45 | Cite as

Extended harmonic analysis of phase space representations for the Galilei group

  • S. Twareque Ali
  • Eduard Prugovečki
Article

Abstract

The spectral resolution of phase space representations of the Galilei group is achieved by deriving all possible decompositions into irreducible representations corresponding to reproducing kernel Hilbert spaces. Spectral syntheses in terms of eigenfunction expansions, as well as in terms of continuous resolutions of the identity, are achieved. For the latter, the existence, uniqueness and other basic properties of resolution generators are established. This is shown to lead to systems of covariance related to measurements of stochastic phase space values performed with extended quantum test particles, whose proper wavefunctions are the aforementioned resolution generators.

AMS (MOS) subject classifications

20C35 81G20 

Key words

Harmonic analysis stochastic quantum mechanics systems of covariance 

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Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • S. Twareque Ali
    • 1
  • Eduard Prugovečki
    • 2
  1. 1.Department of MathematicsConcordia UniversityMontrealCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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