Overview

The book is essentially based on recent work of the authors. In order to unify and generalize the results obtained so far, new concepts have been introduced, e.g., an infinite order chain representation of the continued fraction expansion of irrationals, the conditional measures associated with, and the extended random variables corresponding to that representation. Also, such procedures as singularization and insertion allow to obtain most of the continued fraction expansions related to the regular continued fraction expansion. The authors present and prove with full details for the first time in book form, the most recent developments in solving the celebrated 1812 Gauss' problem which originated the metrical theory of continued fractions. At the same time, they study exhaustively the Perron-Frobenius operator, which is of basic importance in this theory, on various Banach spaces including that of functions of bounded variation on the unit interval.The book is of interest to research workers and advanced Ph.D. students in probability theory, stochastic processes and number theory.

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9789048161300

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Reviews

"From the reviews: ""The authors present and prove the most recent developments in solving the celebrated 1812 Gauss’ problem which originated the metrical theory of continued fractions. At the same time, they study exhaustively the Perron-Frobenius operator, which is of basic importance in this theory, on various Banach spaces including that of functions of bounded variation on the unit interval. The book is of interest to research workers and advanced Ph. D. students in probability theory, stochastic processes and number theory."" (Cryssoula Ganatsiou, Zentralblatt MATH, Vol. 1069 (20), 2005) ""While many excellent books on continued fractions are written, it is rare to see a book exclusively devoted to the material theory of these objects. … In addition to filling a hole in the mathematical literature, it does this very thoroughly. It gets around most topics related to the metrical theory of continued fractions … . The book is well suited for researchers and advanced graduate students working in functional analysis, probability and/or ergodic theory wishing to learn about the world of continued fractions."" (Simon Kristensen, Zentralblatt MATH, Vol. 1122 (24), 2007)"

From the reviews: The authors present and prove the most recent developments in solving the celebrated 1812 Gauss' problem which originated the metrical theory of continued fractions. At the same time, they study exhaustively the Perron-Frobenius operator, which is of basic importance in this theory, on various Banach spaces including that of functions of bounded variation on the unit interval. The book is of interest to research workers and advanced Ph. D. students in probability theory, stochastic processes and number theory. (Cryssoula Ganatsiou, Zentralblatt MATH, Vol. 1069 (20), 2005) While many excellent books on continued fractions are written, it is rare to see a book exclusively devoted to the material theory of these objects. ! In addition to filling a hole in the mathematical literature, it does this very thoroughly. It gets around most topics related to the metrical theory of continued fractions ! . The book is well suited for researchers and advanced graduate students working in functional analysis, probability and/or ergodic theory wishing to learn about the world of continued fractions. (Simon Kristensen, Zentralblatt MATH, Vol. 1122 (24), 2007)

From the reviews: The authors present and prove the most recent developments in solving the celebrated 1812 Gauss' problem which originated the metrical theory of continued fractions. At the same time, they study exhaustively the Perron-Frobenius operator, which is of basic importance in this theory, on various Banach spaces including that of functions of bounded variation on the unit interval. The book is of interest to research workers and advanced Ph. D. students in probability theory, stochastic processes and number theory. (Cryssoula Ganatsiou, Zentralblatt MATH, Vol. 1069 (20), 2005) While many excellent books on continued fractions are written, it is rare to see a book exclusively devoted to the material theory of these objects. ... In addition to filling a hole in the mathematical literature, it does this very thoroughly. It gets around most topics related to the metrical theory of continued fractions ... . The book is well suited for researchers and advanced graduate students working in functional analysis, probability and/or ergodic theory wishing to learn about the world of continued fractions. (Simon Kristensen, Zentralblatt MATH, Vol. 1122 (24), 2007)

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