Metrical theory of continued fractions

Description

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.

Subjects

Series Statement

• Mathematics and its applications -- v. 547
• Mathematics and its applications (Kluwer Academic Publishers) -- v. 547.

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Other Editions

• Metrical theory of continued fractionsKluwer Academic Publishers2002-01-01
• Metrical Theory of Continued Fractions (Mathematics and Its Applications)HardcoverSpringer2002-09-30
• Metrical Theory of Continued FractionspaperbackSpringer Netherlands2010-12-08
• Metrical Theory of Continued FractionsSpringer2013-01-01
• Metrical Theory of Continued FractionsPaperbackSpringer2014-03-14