Transformations with highly nonhomogeneous spectrum of finite multiplicity
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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.
KeywordsErgodic Theory Ergodic Measure Finite Abelian Group Multiplicity Function Measure Preserve Transformation
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