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Warianty tytułu
Języki publikacji
Abstrakty
We study spectral properties of Anzai skew products $T_{φ}: 𝕋² → 𝕋²$ defined by
$T_{φ}(z,ω) = (e^{2πiα}z,φ(z)ω)$,
where α is irrational and φ: 𝕋 → 𝕋 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.
$T_{φ}(z,ω) = (e^{2πiα}z,φ(z)ω)$,
where α is irrational and φ: 𝕋 → 𝕋 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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
1-13
Opis fizyczny
Daty
wydano
2001
Twórcy
autor
- Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-1-1
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