Israel Journal of Mathematics

, Volume 56, Issue 1, pp 75–88 | Cite as

Transformations with highly nonhomogeneous spectrum of finite multiplicity

  • E. Arthur Robinson


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.


Ergodic Theory Ergodic Measure Finite Abelian Group Multiplicity Function Measure Preserve Transformation 
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Copyright information

© Hebrew University 1986

Authors and Affiliations

  • E. Arthur Robinson
    • 1
  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

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