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Metrical Theory of Continued Fractions - M. Iosifescu, Cor Kraaikamp

Metrical Theory of Continued Fractions

Buch | Hardcover
383 Seiten
2002 | 2002 ed.
Springer-Verlag New York Inc.
978-1-4020-0892-4 (ISBN)
CHF 179,70 inkl. MwSt
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. n, we have w = lim [al(w),··· , an(w)], w E 0, n--->oo thus explaining the name of T.
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.

1 Basic properties of the continued fraction expansion.- 2 Solving Gauss’ problem.- 3 Limit theorems.- 4 Ergodic theory of continued fractions.- Appendix 1: Spaces, functions, and measures.- A1.1.- A1.2.- A1.3.- A1.4.- A1.5.- A1.6.- Appendix 2: Regularly varying functions.- A2.1.- A2.2.- A2.3.- Appendix 3: Limit theorems for mixing random variables.- A3.1.- A3.2.- A3.3.- Notes and Comments.- References.

Erscheint lt. Verlag 30.9.2002
Reihe/Serie Mathematics and Its Applications ; 547
Mathematics and Its Applications ; 547
Zusatzinfo XIX, 383 p.
Verlagsort New York, NY
Sprache englisch
Maße 156 x 234 mm
Themenwelt Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
ISBN-10 1-4020-0892-9 / 1402008929
ISBN-13 978-1-4020-0892-4 / 9781402008924
Zustand Neuware
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