Singular points of a self-similar function of spectral order zero: self-similar Stieltjes string
type: Item
instance of: scholarly article
title: Singular points of a self-similar function of spectral order zero: self-similar Stieltjes string
zbMATH Open document ID: 1242.28015
DOI: 10.1134/S0001434610070254
author: I. A. Sheipak
published in: Mathematical Notes
publication date: 2011-11-25T00:00:00Z
review text: The author defines self-similar functions as fixed points for similarity operators. These operators are compositions of piecewise shifts, dilations and renormalizations. The spectral order of a function is defined in terms of the renormalization coefficients. Some basic properties of self-similar functions are studied: when are they piecewise constant, when are they non-decreasing.
reviewed by: Dorin Ervin Dutkay
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 5980669
zbMATH Keywords: self-similar function
zbMATH Keywords: spectral order
zbMATH Keywords: Stieltjes string
zbMATH Keywords: singular point
zbMATH Keywords: self-similar measure
zbMATH Keywords: similarity operators
MaRDI profile type: Publication
cites work: On a Spectral Problem Related to Self-Similar Measures
cites work: Self-similar functions in $ L_2\lbrack0,1\rbrack$ and the Sturm-Liouville problem with a singular indefinite weight
cites work: Asymptotics of the eigenvalues of the Sturm-Liouville problem with discrete self-similar weight
cites work: Sur une courbe plane
cites work: Sur les courbes limités de polygones obtenus par trisection
cites work: Refinement equations with nonnegative coefficients
cites work: Fractal curves and wavelets
cites work: Q5695302
full work available at URL: s0001434610070254
OpenAlex ID: W2044757245
description: scientific article; zbMATH DE number 5980669