Summary
Conditions have been given [7] under which a special automorphism over an automorphism admitting a simple approximation again admits a simple approximation, and so has simple spectrum.
In this paper using different techniques to those employed in [7], we obtain improved results in the same direction. Specifically, conditions are given for a special automorphism over an automorphism, which admits either a simple approximation, or an approximation with suitable speed, to have bounded spectral multiplicity. Furthermore, we obtain as a corollary a result on primitive automorphisms, which partially generalises a result appearing in [4].
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Goodson, G.R., Whitman, P.N. Approximation and the spectral multiplicity of special automorphisms. Z. Wahrscheinlichkeitstheorie verw Gebiete 49, 155–162 (1979). https://doi.org/10.1007/BF00534254
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DOI: https://doi.org/10.1007/BF00534254