000063082 001__ 63082 000063082 005__ 20190709135457.0 000063082 0247_ $$2doi$$a10.1017/S0013091516000316 000063082 0248_ $$2sideral$$a99782 000063082 037__ $$aART-2017-99782 000063082 041__ $$aeng 000063082 100__ $$aViswanathan, P. 000063082 245__ $$aA fractal operator on some standard spaces of functions 000063082 260__ $$c2017 000063082 5060_ $$aAccess copy available to the general public$$fUnrestricted 000063082 5203_ $$aThrough 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 a-fractal operator on (Figure presented.), 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 (Figure presented.) of all bounded functions and the Lebesgue space (Figure presented.), and in some standard spaces of smooth functions such as the space (Figure presented.) of k-times continuously differentiable functions, Hölder spaces (Figure presented.) and Sobolev spaces (Figure presented.). Using properties of the a-fractal operator, the existence of Schauder bases consisting of self-referential functions for these function spaces is established. 000063082 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000063082 590__ $$a0.604$$b2017 000063082 591__ $$aMATHEMATICS$$b201 / 309 = 0.65$$c2017$$dQ3$$eT2 000063082 592__ $$a0.695$$b2017 000063082 593__ $$aMathematics (miscellaneous)$$c2017$$dQ2 000063082 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000063082 700__ $$0(orcid)0000-0003-4847-0493$$aNavascués, M.A.$$uUniversidad de Zaragoza 000063082 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000063082 773__ $$g60, 3 (2017), 771-776 [17 pp]$$pProc. Edinb. Math. Soc.$$tPROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY$$x0013-0915 000063082 8564_ $$s602364$$uhttps://zaguan.unizar.es/record/63082/files/texto_completo.pdf$$yPostprint 000063082 8564_ $$s71514$$uhttps://zaguan.unizar.es/record/63082/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000063082 909CO $$ooai:zaguan.unizar.es:63082$$particulos$$pdriver 000063082 951__ $$a2019-07-09-11:44:17 000063082 980__ $$aARTICLE