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Труды Математического института имени В. А. Стеклова, 2000, том 231, страницы 5–45
(Mi tm510)
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Эта публикация цитируется в 64 научных статьях (всего в 64 статьях)
On the Spectrum of Hecke Type Operators Related to Some Fractal Groups
L. Bartholdia, R. I. Grigorchukb a University of Geneva
b Steklov Mathematical Institute, Russian Academy of Sciences
Аннотация:
We give the first example of a connected 4-regular graph whose Laplace operator's spectrum is a Cantor set, as well as several other computations of spectra following a common “finite approximation” method. These spectra are simple transforms of the Julia sets associated to some quadratic maps. The graphs involved are Schreier graphs of fractal groups of intermediate growth, and are also “substitutional graphs”. We also formulate our results in terms of Hecke type operators related to some irreducible quasi-regular representations of fractal groups and in terms of the Markovian operator associated to noncommutative dynamical systems via which these fractal groups were originally defined in \cite {grigorchuk:burnside}.\lb In the computations we performed, the self-similarity of the groups is reflected in the self-similarity of some operators; they are approximated by finite counterparts whose spectrum is computed by an ad hoc factorization process.
Поступило в ноябре 1999 г.
Образец цитирования:
L. Bartholdi, R. I. Grigorchuk, “On the Spectrum of Hecke Type Operators Related to Some Fractal Groups”, Динамические системы, автоматы и бесконечные группы, Сборник статей, Труды МИАН, 231, Наука, МАИК «Наука/Интерпериодика», М., 2000, 5–45; Proc. Steklov Inst. Math., 231 (2000), 1–41
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tm510 https://www.mathnet.ru/rus/tm/v231/p5
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