Metrical Theory of Continued Fractions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2002
|
| Schriftenreihe: | Mathematics and Its Applications
547 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real numbers. We have attempted to give the best possible results known so far, with proofs which are the simplest and most direct. The book has had a long gestation period because we first decided to write it in March 1994. This gave us the possibility of essentially improving the initial versions of many parts of it. Even if the two authors are different in style and approach, every effort has been made to hide the differences. Let 0 denote the set of irrationals in I = [0,1]. Define the (reg ular) continued fraction transformation T by T (w) = fractional part of n 1/w, w E O. Write T for the nth iterate of T, n E N = {O, 1, ... }, n 1 with TO = identity map. The positive integers an(w) = al(T - (W)), n E N+ = {1,2··· }, where al(w) = integer part of 1/w, w E 0, are called the (regular continued fraction) digits of w. Writing . for arbitrary indeterminates Xi, 1 :::; i :::; n, we have w = lim [al(w),··· , an(w)], w E 0, n--->oo thus explaining the name of T. The above equation will be also written as w = lim [al(w), a2(w),···], w E O. |
| Beschreibung: | 1 Online-Ressource (XIX, 383 p) |
| ISBN: | 9789401599405 9789048161300 |
| DOI: | 10.1007/978-94-015-9940-5 |
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| 490 | 0 | |a Mathematics and Its Applications |v 547 | |
| 500 | |a This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real numbers. We have attempted to give the best possible results known so far, with proofs which are the simplest and most direct. The book has had a long gestation period because we first decided to write it in March 1994. This gave us the possibility of essentially improving the initial versions of many parts of it. Even if the two authors are different in style and approach, every effort has been made to hide the differences. Let 0 denote the set of irrationals in I = [0,1]. Define the (reg ular) continued fraction transformation T by T (w) = fractional part of n 1/w, w E O. Write T for the nth iterate of T, n E N = {O, 1, ... }, n 1 with TO = identity map. The positive integers an(w) = al(T - (W)), n E N+ = {1,2··· }, where al(w) = integer part of 1/w, w E 0, are called the (regular continued fraction) digits of w. Writing . for arbitrary indeterminates Xi, 1 :::; i :::; n, we have w = lim [al(w),··· , an(w)], w E 0, n--->oo thus explaining the name of T. The above equation will be also written as w = lim [al(w), a2(w),···], w E O. | ||
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Datensatz im Suchindex
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| author | Iosifescu, Marius |
| author_facet | Iosifescu, Marius |
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| bvnumber | BV042424177 |
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| ctrlnum | (OCoLC)864065594 (DE-599)BVBBV042424177 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9940-5 |
| format | Electronic eBook |
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| id | DE-604.BV042424177 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401599405 9789048161300 |
| language | English |
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| spelling | Iosifescu, Marius Verfasser aut Metrical Theory of Continued Fractions by Marius Iosifescu, Cor Kraaikamp Dordrecht Springer Netherlands 2002 1 Online-Ressource (XIX, 383 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 547 This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real numbers. We have attempted to give the best possible results known so far, with proofs which are the simplest and most direct. The book has had a long gestation period because we first decided to write it in March 1994. This gave us the possibility of essentially improving the initial versions of many parts of it. Even if the two authors are different in style and approach, every effort has been made to hide the differences. Let 0 denote the set of irrationals in I = [0,1]. Define the (reg ular) continued fraction transformation T by T (w) = fractional part of n 1/w, w E O. Write T for the nth iterate of T, n E N = {O, 1, ... }, n 1 with TO = identity map. The positive integers an(w) = al(T - (W)), n E N+ = {1,2··· }, where al(w) = integer part of 1/w, w E 0, are called the (regular continued fraction) digits of w. Writing . for arbitrary indeterminates Xi, 1 :::; i :::; n, we have w = lim [al(w),··· , an(w)], w E 0, n--->oo thus explaining the name of T. The above equation will be also written as w = lim [al(w), a2(w),···], w E O. Mathematics Operator theory Computer science / Mathematics Number theory Distribution (Probability theory) Probability Theory and Stochastic Processes Number Theory Operator Theory Computational Mathematics and Numerical Analysis Informatik Mathematik Kraaikamp, Cor Sonstige oth https://doi.org/10.1007/978-94-015-9940-5 Verlag Volltext |
| spellingShingle | Iosifescu, Marius Metrical Theory of Continued Fractions Mathematics Operator theory Computer science / Mathematics Number theory Distribution (Probability theory) Probability Theory and Stochastic Processes Number Theory Operator Theory Computational Mathematics and Numerical Analysis Informatik Mathematik |
| title | Metrical Theory of Continued Fractions |
| title_auth | Metrical Theory of Continued Fractions |
| title_exact_search | Metrical Theory of Continued Fractions |
| title_full | Metrical Theory of Continued Fractions by Marius Iosifescu, Cor Kraaikamp |
| title_fullStr | Metrical Theory of Continued Fractions by Marius Iosifescu, Cor Kraaikamp |
| title_full_unstemmed | Metrical Theory of Continued Fractions by Marius Iosifescu, Cor Kraaikamp |
| title_short | Metrical Theory of Continued Fractions |
| title_sort | metrical theory of continued fractions |
| topic | Mathematics Operator theory Computer science / Mathematics Number theory Distribution (Probability theory) Probability Theory and Stochastic Processes Number Theory Operator Theory Computational Mathematics and Numerical Analysis Informatik Mathematik |
| topic_facet | Mathematics Operator theory Computer science / Mathematics Number theory Distribution (Probability theory) Probability Theory and Stochastic Processes Number Theory Operator Theory Computational Mathematics and Numerical Analysis Informatik Mathematik |
| url | https://doi.org/10.1007/978-94-015-9940-5 |
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