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Zero Measure Spectrum for the Almost Mathieu Operator *
| Content Provider | Semantic Scholar |
|---|---|
| Author | Last, Yoram |
| Copyright Year | 1993 |
| Abstract | We study the almost Mathieu operator: 1) + cos(2n +)u(n), on l 2 (Z), and show that for all ; , and (Lebesgue) a.e. , the Lebesgue measure of its spectrum is precisely j4 ? 2jjj. In particular, for jj = 2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational 's (and jj = 2) we show that the Hausdorr dimension of the spectrum is smaller than or equal to 1=2. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://mpej.unige.ch/mp_arc/html/c/93/93-173.ps.gz |
| Alternate Webpage(s) | http://rene.ma.utexas.edu/mp_arc/html/c/93/93-173.ps.gz |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Cantor set Hausdorff dimension |
| Content Type | Text |
| Resource Type | Article |
