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Transformations with highly nonhomogeneous spectrum of finite multiplicity

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Abstract

This paper studies a spectral invariant ℳ T for ergodic measure preserving transformationsT called theessential spectral multiplicities. It is defined as the essential range of the multiplicity function for the induced unitary operatorU T. Examples are constructed where ℳ T is subject only to the following conditions: (i) 1∈ℳ T , (ii) lcm(n, m)∈ℳ T wherevern, m ∈ ℳ T , and (iii) sup ℳ T <+∞. This shows thatD T, definedD T=card ℳ T , may be an arbitrary positive integer. The results are obtained by an algebraic construction together with approximation arguments.

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Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, 19104, Philadelphia, PA, USA

    E. Arthur Robinson

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  1. E. Arthur Robinson
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Additional information

This research was partially supported by NSF grant MCS 8102790.

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Robinson, E.A. Transformations with highly nonhomogeneous spectrum of finite multiplicity. Israel J. Math. 56, 75–88 (1986). https://doi.org/10.1007/BF02776241

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  • DOI: https://doi.org/10.1007/BF02776241

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