000125872 001__ 125872
000125872 005__ 20240319080950.0
000125872 0247_ $$2doi$$a10.1142/S0218348X2272001X
000125872 0248_ $$2sideral$$a128810
000125872 037__ $$aART-2022-128810
000125872 041__ $$aeng
000125872 100__ $$0(orcid)0000-0003-4847-0493$$aNavascues, M. A.$$uUniversidad de Zaragoza
000125872 245__ $$aA Revisit to stability of schauder bases: Fractalizing multivariate faber-schauder system
000125872 260__ $$c2022
000125872 5060_ $$aAccess copy available to the general public$$fUnrestricted
000125872 5203_ $$aLet X be a Banach space with a Schauder basis (xm)m=08, and I be the identity operator on X. It is known, at least in essence, that if (Tm)m=08 is a sequence of bounded linear operators on X such that am=08aI-T ma < 8, then (Tm(xm))m=08 is also a basis. The first part of this work acts as an expository note to formally record the aforementioned stability result. In the second part, we apply this stability result to construct a Schauder basis consisting of bivariate fractal functions for the space of continuous functions defined on a rectangle. To this end, fractal perturbations of the elements in the classical bivariate Faber-Schauder system are formulated using a sequence of bounded linear fractal operators close to the identity operator in accordance with the stability result mentioned above. This illustration, although emphasized only for the bivariate case, can easily be extended to higher dimensions. Further, the perturbation technique used here acts as a companion for a few researches on fractal bases in the univariate setting. © 2022 World Scientific Publishing Company.
000125872 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000125872 590__ $$a4.7$$b2022
000125872 592__ $$a0.6$$b2022
000125872 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b11 / 107 = 0.103$$c2022$$dQ1$$eT1
000125872 593__ $$aMultidisciplinary$$c2022$$dQ1
000125872 591__ $$aMULTIDISCIPLINARY SCIENCES$$b21 / 73 = 0.288$$c2022$$dQ2$$eT1
000125872 593__ $$aModeling and Simulation$$c2022$$dQ2
000125872 593__ $$aApplied Mathematics$$c2022$$dQ2
000125872 593__ $$aGeometry and Topology$$c2022$$dQ2
000125872 594__ $$a6.6$$b2022
000125872 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000125872 700__ $$aViswanathan, P.
000125872 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000125872 773__ $$g30, 3 (2022), 2272001 - 908$$pFractals-Complex Geom. Patterns Scaling Nat. Soc.$$tFractals$$x0218-348X
000125872 8564_ $$s9182910$$uhttps://zaguan.unizar.es/record/125872/files/texto_completo.pdf$$yPostprint
000125872 8564_ $$s1330206$$uhttps://zaguan.unizar.es/record/125872/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000125872 909CO $$ooai:zaguan.unizar.es:125872$$particulos$$pdriver
000125872 951__ $$a2024-03-18-12:58:23
000125872 980__ $$aARTICLE