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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Metrical Theory of Continued Fractions (Paperback, Softcover reprint of hardcover 1st ed. 2002)
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Metrical Theory of Continued Fractions (Paperback, Softcover reprint of hardcover 1st ed. 2002)
Series: Mathematics and Its Applications, 547
Expected to ship within 18 - 22 working days
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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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