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  1. Journal of Fourier Analysis and Applications
  2. Journal of Fourier Analysis and Applications : Volume 6
  3. Journal of Fourier Analysis and Applications : Volume 6, Issue 1, January 2000
  4. Refinement equations with nonnegative coefficients
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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 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 6, Issue 6, November 2000
Journal of Fourier Analysis and Applications : Volume 6, Issue 5, September 2000
Journal of Fourier Analysis and Applications : Volume 6, Issue 4, July 2000
Journal of Fourier Analysis and Applications : Volume 6, Issue 3, May 2000
Journal of Fourier Analysis and Applications : Volume 6, Issue 2, March 2000
Journal of Fourier Analysis and Applications : Volume 6, Issue 1, January 2000
Editorial statement
Designing local orthogonal bases on finite groups I: Abelian case
Reconstruction from limited data of arc means
Pompeiu sets in compact Heisenberg manifolds
Refinement equations with nonnegative coefficients
Finite-dimensional approximation of the inverse frame operator
Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces
A generalized hecke identity
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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Refinement equations with nonnegative coefficients

Content Provider SpringerLink
Author Protasov, Vladimir
Copyright Year 2000
Abstract In this paper we analyze solutions of the n-scale functional equation Ф(x) = Σk∈ℤ Pk Ф(nx−k), where n≥2 is an integer, the coefficients {Pk} are nonnegative and Σpk = 1. We construct a sharp criterion for the existence of absolutely continuous solutions of bounded variation. This criterion implies several results concerning the problem of integrable solutions of n-scale refinement equations and the problem of absolutely continuity of distribution function of one random series. Further we obtain a complete classification of refinement equations with positive coefficients (in the case of finitely many terms) with respect to the existence of continuous or integrable compactly supported solutions.
Starting Page 55
Ending Page 78
Page Count 24
File Format PDF
ISSN 10695869
Journal Journal of Fourier Analysis and Applications
Volume Number 6
Issue Number 1
e-ISSN 15315851
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2000-01-01
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword refinement equation Fourier series tree distributions joint spectral radius Abstract Harmonic Analysis Approximations and Expansions Fourier Analysis Partial Differential Equations Applications of Mathematics Signal, Image and Speech Processing
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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