On the discrepancy of some generalized Kakutani's sequences of partitions
| dc.contributor.author | Drmota, Michael | |
| dc.contributor.author | Infusino, Maria | |
| dc.date.accessioned | 2020-05-26T12:28:50Z | |
| dc.date.available | 2020-05-26T12:28:50Z | |
| dc.date.issued | 2012 | eng |
| dc.description.abstract | In this paper we study a class of generalized Kakutani’s sequences of partitionsof [0,1],constructedbyusingthetechniqueofsuccessive ρ−refinements. Our main focus is to derive bounds for the discrepancy of these sequences. The approach that we use is based on a tree representation of the sequence of partitions which is precisely the parsing tree generated by Khodak’s coding algorithm. With the help of this technique we derive (partly up to a logarithmic factor) optimal upper bound in the so-called rational case. The upper bounds in the irrational case that we obtain are weaker, since they heavily depend on Diophantine approximation properties of a certain irrational number. Finally, we present an application of these results to a class of fractals. | eng |
| dc.description.version | published | eng |
| dc.identifier.uri | https://kops.uni-konstanz.de/handle/123456789/49646 | |
| dc.language.iso | eng | eng |
| dc.rights | terms-of-use | |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | |
| dc.subject.ddc | 510 | eng |
| dc.title | On the discrepancy of some generalized Kakutani's sequences of partitions | eng |
| dc.type | JOURNAL_ARTICLE | eng |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @article{Drmota2012discr-49646,
year={2012},
title={On the discrepancy of some generalized Kakutani's sequences of partitions},
url={https://math.boku.ac.at/udt/vol07/no1/04DrmInf.pdf},
number={1},
volume={7},
journal={Uniform Distribution Theory},
pages={75--104},
author={Drmota, Michael and Infusino, Maria}
} | |
| kops.citation.iso690 | DRMOTA, Michael, Maria INFUSINO, 2012. On the discrepancy of some generalized Kakutani's sequences of partitions. In: Uniform Distribution Theory. Mathematical Institute of the Slovak Academy of Sciences. 2012, 7(1), pp. 75-104. eISSN 1336-913X | deu |
| kops.citation.iso690 | DRMOTA, Michael, Maria INFUSINO, 2012. On the discrepancy of some generalized Kakutani's sequences of partitions. In: Uniform Distribution Theory. Mathematical Institute of the Slovak Academy of Sciences. 2012, 7(1), pp. 75-104. eISSN 1336-913X | eng |
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| kops.sourcefield | Uniform Distribution Theory. Mathematical Institute of the Slovak Academy of Sciences. 2012, <b>7</b>(1), pp. 75-104. eISSN 1336-913X | deu |
| kops.sourcefield.plain | Uniform Distribution Theory. Mathematical Institute of the Slovak Academy of Sciences. 2012, 7(1), pp. 75-104. eISSN 1336-913X | deu |
| kops.sourcefield.plain | Uniform Distribution Theory. Mathematical Institute of the Slovak Academy of Sciences. 2012, 7(1), pp. 75-104. eISSN 1336-913X | eng |
| kops.url | https://math.boku.ac.at/udt/vol07/no1/04DrmInf.pdf | eng |
| kops.urlDate | 2020-05-26 | eng |
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| source.bibliographicInfo.fromPage | 75 | eng |
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| source.bibliographicInfo.toPage | 104 | eng |
| source.bibliographicInfo.volume | 7 | eng |
| source.identifier.eissn | 1336-913X | eng |
| source.periodicalTitle | Uniform Distribution Theory | eng |
| source.publisher | Mathematical Institute of the Slovak Academy of Sciences | eng |