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Multiplicity, rank pairs

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Abstract

For any pair(m, r) such that2 ≤ m ≤ r > ∞, we construct an ergodic dynamical system having spectral multiplicitym and rankr. The essential range of the multiplicity function is described. Ifr ≥ 2, the pair(m, r) also has a weakly mixing realization.

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Authors and Affiliations

  1. Institute of Mathematics Nicholas, Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland

    J. Kwiatkowski

  2. Département de Mathématiques, U.B.O., Fac. des Sciences, 6 Avenue V. Le Gorgeu, B. P. 809, 29285, Brest Cedex, France

    Y. Lacroix

Authors
  1. J. Kwiatkowski
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  2. Y. Lacroix
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Correspondence to J. Kwiatkowski.

Additional information

Supported by KBN grant no. 2 P30103107. The author acknowledges the hospitality of the Mathematics Department of Université de Bretagne Occidentale, Brest, where this paper was written.

Supported by C.A.F. Nord Finistère.

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Kwiatkowski, J., Lacroix, Y. Multiplicity, rank pairs. J. Anal. Math. 71, 205–235 (1997). https://doi.org/10.1007/BF02788031

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  • DOI: https://doi.org/10.1007/BF02788031

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