MARTINGALE DIFFERENCES AND THE METRIC THEORY OF CONTINUED FRACTIONS

被引：0
|
作者：
Haynes, Alan K. [1 ]
Vaaler, Jeffrey D. [1 ]
机构：
[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA
来源：
ILLINOIS JOURNAL OF MATHEMATICS | 2008年 / 52卷 / 01期
关键词：
D O I：
10.1215/ijm/1242414129
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate a collection of orthonormal functions that encodes information about the continued fraction expansion of real numbers. When suitably ordered these functions form a complete system of martingale differences and are a special case of a class of martingale differences considered by Gundy. By applying known results for martingales, we obtain corresponding metric theorems for the continued fraction expansion of almost all real numbers.
引用
收藏
页码：213 / 242
页数：30
相关论文
共 50 条
  • [1] Metric theory for continued β-fractions
    Feng, Jing
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 542 (01)
  • [2] Quantitative metric theory of continued fractions
    J HANČL
    A HADDLEY
    P LERTCHOOSAKUL
    R NAIR
    Proceedings - Mathematical Sciences, 2016, 126 : 167 - 177
  • [3] Quantitative metric theory of continued fractions
    Hancl, J.
    Haddley, A.
    Lertchoosakul, P.
    Nair, R.
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2016, 126 (02): : 167 - 177
  • [4] ON THE METRIC THEORY OF NEAREST INTEGER CONTINUED FRACTIONS
    RIESEL, H
    BIT, 1987, 27 (02): : 248 - 263
  • [5] ON THE METRIC THEORY OF CONTINUED FRACTIONS IN POSITIVE CHARACTERISTIC
    Lertchoosakul, Poj
    Nair, Radhakrishnan
    MATHEMATIKA, 2014, 60 (02) : 307 - 320
  • [6] METRIC THEORY OF CONTINUED FRACTIONS BY NEAREST INTEGERS
    RIEGER, GJ
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (02): : A270 - A270
  • [7] On the metric theory of p-adic continued fractions
    Hancl, J.
    Jassova, A.
    Lertchoosakul, P.
    Nair, R.
    INDAGATIONES MATHEMATICAE-NEW SERIES, 2013, 24 (01): : 42 - 56
  • [8] ON THE QUANTITATIVE METRIC THEORY OF CONTINUED FRACTIONS IN POSITIVE CHARACTERISTIC
    Lertchoosakul, Poj
    Nair, Radhakrishnan
    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2018, 61 (01) : 283 - 293
  • [9] METRIC THEORY of PARTIAL QUOTIENTS of N-CONTINUED FRACTIONS
    Wang, Jinfeng
    Zhang, Yuan
    Fractals, 2022, 30 (01):
  • [10] METRIC THEORY OF PARTIAL QUOTIENTS OF N-CONTINUED FRACTIONS
    Wang, Jinfeng
    Zhang, Yuan
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2022, 30 (01)
12345