Ergodic measure preserving transformations with arbitrary finite spectral multiplicities

Robinson, E. Arthur

doi:10.1007/bf01389325

“…Spectral analysis of double extensions of T . The spectral analysis of a double extension of T given below is similar to Robinson's analysis in [29] and [30].…”

Section: 1mentioning

confidence: 74%

“…It has already been shown that all subsets containing 1 are realizable [19] (reproved by a different argument in [3]). For more information on the subject see also earlier articles by Robinson [29], [30], and the surveys [11,18]. Less is known about Koopman realization of sets which do not contain 1.…”

mentioning

confidence: 99%

Some new cases of realization of spectral multiplicity function for ergodic transformations

Katok

¹

,

Lemańczyk

²

2009

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“…His example involved an exchange of 30 intervals and had maximal spectral multiplicity lying between 2 and 30. Robinson [7] and Katok (unpublished) generalised his result again using interval exchange transformations.…”

Section: Introductionmentioning

confidence: 86%

On the spectral multiplicity of a class of finite rank transformations

Goodson¹

1985

Proc. Amer. Math. Soc.

8

0

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ABSTRACT. The rank M transformations, which Chacon called the simple approximations with multiplicity M, were shown by Chacon to have maximal spectral multiplicity at most M, although no example was given where this bound is attained for M > 1. In this paper, for each natural number M > 1, we show how to construct a simple approximation with multiplicity M which is ergodic and has maximal spectral multiplicity equal to M -1. Introduction.The purpose of this paper is to give a method of constructing ergodic automorphisms t: [0,1) -> [0,1) with finite rank and maximal spectral multiplicity greater than one. In particular for each natural number M > 1 we show how to' construct ergodic automorphisms which admit simple approximations with multiplicity M (in the sense of Chacon [2]) and have maximal spectral multiplicity

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“…If, for UT, the eigenvalue 1 is simple and is the only eigenvalue, we say r has continuous spectrum. (See Robinson [7] and Parry [6] for more details and a discussion of the history of the spectral theory of measure preserving transformations.) DEFINITION 2.…”

Section: Preliminariesmentioning

confidence: 99%

On the Spectral Multiplicity of a Class of Finite Rank Transformations

Goodson¹

1985

Proceedings of the American Mathematical Society

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ABSTRACT. The rank M transformations, which Chacon called the simple approximations with multiplicity M, were shown by Chacon to have maximal spectral multiplicity at most M, although no example was given where this bound is attained for M > 1. In this paper, for each natural number M > 1, we show how to construct a simple approximation with multiplicity M which is ergodic and has maximal spectral multiplicity equal to M -1. Introduction.The purpose of this paper is to give a method of constructing ergodic automorphisms t: [0,1) -> [0,1) with finite rank and maximal spectral multiplicity greater than one. In particular for each natural number M > 1 we show how to' construct ergodic automorphisms which admit simple approximations with multiplicity M (in the sense of Chacon [2]) and have maximal spectral multiplicity

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Ergodic measure preserving transformations with arbitrary finite spectral multiplicities

Cited by 49 publications

References 14 publications

Some new cases of realization of spectral multiplicity function for ergodic transformations

Some new cases of realization of spectral multiplicity function for ergodic transformations

On the spectral multiplicity of a class of finite rank transformations

On the Spectral Multiplicity of a Class of Finite Rank Transformations

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