Skip to main content
    • Aa
    • Aa

Continued fractions and Fourier transforms

  • R. Kaufman (a1)

Let FN be the set of real numbers x whose continued fraction expansion x = [a0; a1, a2,…, an,…] contains only elements ai = 1,2,…, N. Here N ≥ 2. Considerable effort, [1,3], has centred on metrical properties of FN and certain measures carried by FN. A classification of sets of measure zero, as venerable as the dimensional theory, depends on Fourier-Stieltjes transforms: a closed set E of real numbers is called an M0-set, if E carries a probability measure λ whose transform vanishes at infinity. Aside from the Riemann-Lebesgue Lemma, no purely metrical property of E can ensure that E is an M0-set. For the sets FN, however, metrical properties can be used to construct the measure λ.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1. I. J. Good . “The fractional dimensional theory of continued fractions”, Proc. Cambridge Phil. Soc., 37 (1941), 199228.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 27 *
Loading metrics...

Abstract views

Total abstract views: 86 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th June 2017. This data will be updated every 24 hours.