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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm238https://doi.org/10.1070/sm1997v188n08ABEH000238 https://www.mathnet.ru/eng/sm/v188/i8/p13
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Abstract page: | 336 | Russian version PDF: | 166 | English version PDF: | 10 | References: | 64 | First page: | 1 |
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