Some examples of cocycles with simple continuous singular spectrum

K. Frączek. "Some examples of cocycles with simple continuous singular spectrum." Studia Mathematica 146.1 (2001): 1-13. <http://eudml.org/doc/284426>.

@article{K2001,
abstract = {We study spectral properties of Anzai skew products $T_\{φ\}: ² → ²$ defined by $T_\{φ\}(z,ω) = (e^\{2πiα\}z,φ(z)ω)$, where α is irrational and φ: → is a measurable cocycle. Precisely, we deal with the case where φ is piecewise absolutely continuous such that the sum of all jumps of φ equals zero. It is shown that the simple continuous singular spectrum of $T_\{φ\}$ on the orthocomplement of the space of functions depending only on the first variable is a “typical” property in the above-mentioned class of cocycles, if α admits a sufficiently fast approximation.},
author = {K. Frączek},
journal = {Studia Mathematica},
keywords = {cocycles; Anzai skew product; automorphism; simple continuous singular spectrum},
language = {eng},
number = {1},
pages = {1-13},
title = {Some examples of cocycles with simple continuous singular spectrum},
url = {http://eudml.org/doc/284426},
volume = {146},
year = {2001},
}

TY - JOUR
AU - K. Frączek
TI - Some examples of cocycles with simple continuous singular spectrum
JO - Studia Mathematica
PY - 2001
VL - 146
IS - 1
SP - 1
EP - 13
AB - We study spectral properties of Anzai skew products $T_{φ}: ² → ²$ defined by $T_{φ}(z,ω) = (e^{2πiα}z,φ(z)ω)$, where α is irrational and φ: → is a measurable cocycle. Precisely, we deal with the case where φ is piecewise absolutely continuous such that the sum of all jumps of φ equals zero. It is shown that the simple continuous singular spectrum of $T_{φ}$ on the orthocomplement of the space of functions depending only on the first variable is a “typical” property in the above-mentioned class of cocycles, if α admits a sufficiently fast approximation.
LA - eng
KW - cocycles; Anzai skew product; automorphism; simple continuous singular spectrum
UR - http://eudml.org/doc/284426
ER -