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Sbornik: Mathematics, 1997, Volume 188, Issue 8, Pages 1119–1152
DOI: https://doi.org/10.1070/sm1997v188n08ABEH000238
(Mi sm238)
 

This article is cited in 5 scientific papers (total in 5 papers)

The spectral type of the rearrangements $T_{\alpha,\beta}$

O. N. Ageev

N. E. Bauman Moscow State Technical University
References:
Abstract: A method of geometric models is proposed and applied to the study of the spectral properties of the classical transformations $T_{\alpha,\beta}$. It is proved that the class of ergodic transformations under consideration with absolutely continuous and mixing components contains no transformation with a non-simple spectrum. A criterion for the ergodicity of the transformations $T_{\alpha,\beta}$ is obtained in terms of the geometric models. The multiplicity function of the spectrum of $T_{\alpha ,\beta}$ is determined for any $n$ when $\alpha$ is the golden section.
Received: 21.11.1996
Russian version:
Matematicheskii Sbornik, 1997, Volume 188, Number 8, Pages 13–44
DOI: https://doi.org/10.4213/sm238
Bibliographic databases:
UDC: 517.9
MSC: Primary 28D05, 47A35; Secondary 11K50
Language: English
Original paper language: Russian
Citation: O. N. Ageev, “The spectral type of the rearrangements $T_{\alpha,\beta}$”, Mat. Sb., 188:8 (1997), 13–44; Sb. Math., 188:8 (1997), 1119–1152
Citation in format AMSBIB
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\paper The spectral type of the rearrangements $T_{\alpha,\beta}$
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Linking options:
  • https://www.mathnet.ru/eng/sm238
  • https://doi.org/10.1070/sm1997v188n08ABEH000238
  • https://www.mathnet.ru/eng/sm/v188/i8/p13
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:336
    Russian version PDF:166
    English version PDF:10
    References:64
    First page:1
     
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