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A Fractal Operator on Some Standard Spaces of Functions

Viswanathan, Priya; Navascués, M.A.

Description

Through appropriate choices of elements in the underlying iterated function system, the methodology of fractal interpolation enables us to associate a family of continuous self-referential functions with a prescribed real-valued continuous function on a real compact interval. This procedure elicits what is referred to as an α-fractal operator on , the space of all real-valued continuous functions defined on a compact interval I. With an eye towards connecting fractal functions with other...[Show more]

dc.contributor.authorViswanathan, Priya
dc.contributor.authorNavascués, M.A.
dc.date.accessioned2020-12-20T20:51:28Z
dc.date.available2020-12-20T20:51:28Z
dc.identifier.issn0013-0915
dc.identifier.urihttp://hdl.handle.net/1885/217790
dc.description.abstractThrough appropriate choices of elements in the underlying iterated function system, the methodology of fractal interpolation enables us to associate a family of continuous self-referential functions with a prescribed real-valued continuous function on a real compact interval. This procedure elicits what is referred to as an α-fractal operator on , the space of all real-valued continuous functions defined on a compact interval I. With an eye towards connecting fractal functions with other branches of mathematics, in this paper we continue to investigate the fractal operator in more general spaces such as the space of all bounded functions and the Lebesgue space , and in some standard spaces of smooth functions such as the space of k-times continuously differentiable functions, Hölder spaces and Sobolev spaces . Using properties of the α-fractal operator, the existence of Schauder bases consisting of self-referential functions for these function spaces is established.
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherOxford University Press
dc.sourceProceedings of the Edinburgh Mathematical Society
dc.titleA Fractal Operator on Some Standard Spaces of Functions
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume60
dc.date.issued2017
local.identifier.absfor010108 - Operator Algebras and Functional Analysis
local.identifier.ariespublicationa383154xPUB8517
local.type.statusPublished Version
local.contributor.affiliationViswanathan, Priya, College of Science, ANU
local.contributor.affiliationNavascués, M.A., Universidad de Zaragoza
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage771
local.bibliographicCitation.lastpage786
local.identifier.doi10.1017/S0013091516000316
dc.date.updated2020-11-23T10:05:38Z
local.identifier.scopusID2-s2.0-85008640872
local.identifier.thomsonID000406223200013
CollectionsANU Research Publications

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