We study spectral properties of Anzai skew products defined by , 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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-1-1,
author = {K. Fr\k aczek},
title = {Some examples of cocycles with simple continuous singular spectrum},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {1-13},
zbl = {0970.37008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-1-1}
}
K. Frączek. Some examples of cocycles with simple continuous singular spectrum. Studia Mathematica, Tome 147 (2001) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-1-1/