Abstract
Given a group g it is of some interest to decide which elements of g can be “told apart” by almost periodic functions of g or, which is the same thing (cf. below) by finite dimensional bounded linear representations of g. That is: For two a, b ∈ g we define a ~ b by either of these two properties:
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(I)
For every almost periodic function f(x) in g f(a) = f(b).
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(II)
For every finite dimensional linear unitary representation D(x) of g D(a) = D(b).
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References
J. v. Neumann, Almost periodic functions in a group,Amer. Math. Soc. Trans. 36 (1934), pp. 445–492. To be quoted as “Ap”.
E. P. Wigner, On unitary representations of the inhomogeneous Lorentz group,Annals of Math., 40 (1939), pp. 149–204. Cf. in particular pp. 164–168.
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© 1993 Springer-Verlag Berlin Heidelberg
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von Neumann, J., Wigner, E.P. (1993). Minimally Almost Periodic Groups. In: Wightman, A.S. (eds) The Collected Works of Eugene Paul Wigner. The Collected Works of Eugene Paul Wigner, vol A / 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02781-3_23
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DOI: https://doi.org/10.1007/978-3-662-02781-3_23
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