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  1. Journal of Fourier Analysis and Applications
  2. Journal of Fourier Analysis and Applications : Volume 19
  3. Journal of Fourier Analysis and Applications : Volume 19, Issue 2, April 2013
  4. Patterns in Rational Base Number Systems
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Journal of Fourier Analysis and Applications : Volume 23
Journal of Fourier Analysis and Applications : Volume 22
Journal of Fourier Analysis and Applications : Volume 21
Journal of Fourier Analysis and Applications : Volume 20
Journal of Fourier Analysis and Applications : Volume 19
Journal of Fourier Analysis and Applications : Volume 19, Issue 6, December 2013
Journal of Fourier Analysis and Applications : Volume 19, Issue 5, October 2013
Journal of Fourier Analysis and Applications : Volume 19, Issue 4, August 2013
Journal of Fourier Analysis and Applications : Volume 19, Issue 3, June 2013
Journal of Fourier Analysis and Applications : Volume 19, Issue 2, April 2013
Patterns in Rational Base Number Systems
Note on a Result of Kerman and Weit II
Two-Subspace Projection Method for Coherent Overdetermined Systems
An Analogue of Bochner’s Theorem for Damek-Ricci Spaces
A Note on Reassigned Gabor Spectrograms of Hermite Functions
Generalized Pseudo-Butterworth Refinable Functions
Fourier Transform and Convolutions on L p of a Vector Measure on a Compact Hausdorff Abelian Group
Basic Relations Valid for the Bernstein Space $B^{p}_{\sigma}$ and Their Extensions to Functions from Larger Spaces with Error Estimates in Terms of Their Distances from $B^{p}_{\sigma}$
Wavelet Frame Bijectivity on Lebesgue and Hardy Spaces
Heisenberg Uniqueness Pairs for the Parabola
Multivariate Hörmander-Type Multiplier Theorem for the Hankel transform
Journal of Fourier Analysis and Applications : Volume 19, Issue 1, February 2013
Journal of Fourier Analysis and Applications : Volume 18
Journal of Fourier Analysis and Applications : Volume 17
Journal of Fourier Analysis and Applications : Volume 16
Journal of Fourier Analysis and Applications : Volume 15
Journal of Fourier Analysis and Applications : Volume 14
Journal of Fourier Analysis and Applications : Volume 13
Journal of Fourier Analysis and Applications : Volume 12
Journal of Fourier Analysis and Applications : Volume 11
Journal of Fourier Analysis and Applications : Volume 10
Journal of Fourier Analysis and Applications : Volume 9
Journal of Fourier Analysis and Applications : Volume 8
Journal of Fourier Analysis and Applications : Volume 7
Journal of Fourier Analysis and Applications : Volume 6
Journal of Fourier Analysis and Applications : Volume 5
Journal of Fourier Analysis and Applications : Volume 4
Journal of Fourier Analysis and Applications : Volume 3

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Patterns in Rational Base Number Systems

Content Provider SpringerLink
Author Steiner, Wolfgang Thuswaldner, Jörg M. Morgenbesser, Johannes F.
Copyright Year 2012
Abstract Number systems with a rational number a/b>1 as base have gained interest in recent years. In particular, relations to Mahler’s $\frac{3}{2}$ -problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base a/b and use representations w.r.t. this base to construct normal numbers in base a in the spirit of Champernowne.The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the adèle ring $\mathbb{A}_{\mathbb{Q}}$ and Fourier analysis in $\mathbb{A}_{\mathbb{Q}}$ . With help of these tools we are able to reformulate our results as estimation problems for character sums.
Ending Page 250
Page Count 26
Starting Page 225
File Format PDF
ISSN 10695869
e-ISSN 15315851
Journal Journal of Fourier Analysis and Applications
Issue Number 2
Volume Number 19
Language English
Publisher SP Birkhäuser Verlag Boston
Publisher Date 2012-10-18
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Signal, Image and Speech Processing Rational number system Normal numbers Fractals Fourier analysis, Sum-of-digits function p-adic numbers Abstract Harmonic Analysis Tilings in $n$ dimensions Mathematical Methods in Physics Fourier Analysis Approximations and Expansions Partial Differential Equations Radix representation; digital problems
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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