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On singularity and fine spectral structure of random continued fractions |
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| Authors: | Sergio Albeverio Yuliya Kulyba Mykola Pratsiovytyi Grygoriy Torbin |
| Affiliation: | 1. +49 228 73 34 18+49 228 73 95 37;2. Institut für Angewandte MathematikUniversit?t Bonn, Endenicher Allee 60, 53115 Bonn (Germany);3. HCM,Bonn;4. BiBoS, Bielefeld–Bonn;5. 6. CERFIM, Locarno;7. IZKS, Bonn;8. +380 44 239 30 94+380 44 234 11 08;9. National Dragomanov University, 01601 Kyiv, Ukraine;10. +380 44 239 30 31+380 44 234 11 08;11. National Dragomanov University, Pyrogova str. 9, 01601 Kyiv, Ukraine;12. Institute for Mathematics of NationalAcademy of Sciences of Ukraine, 01601 Kyiv, Ukraine |
| Abstract: | We study properties of the distribution  of a random variable of the continued fraction form  are independent and not necessarily identically distributed random variables. We prove the singularity of  and study the fine spectral structure of such measures. |
| Keywords: | Continued fractions singular probability measures fractals 28A80 11K55 60G30 |