125872 20240319080950.0 doi 10.1142/S0218348X2272001X sideral 128810 ART-2022-128810 eng Navascues, M. A. Universidad de Zaragoza (orcid)0000-0003-4847-0493 A Revisit to stability of schauder bases: Fractalizing multivariate faber-schauder system 2022 Access copy available to the general public Unrestricted Let 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. info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 4.7 2022 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 11 / 107 = 0.103 2022 Q1 T1 MULTIDISCIPLINARY SCIENCES 21 / 73 = 0.288 2022 Q2 T1 0.6 2022 Multidisciplinary 2022 Q1 Modeling and Simulation 2022 Q2 Applied Mathematics 2022 Q2 Geometry and Topology 2022 Q2 6.6 2022 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Viswanathan, P. 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 30, 3 (2022), 2272001 - 908 Fractals-Complex Geom. Patterns Scaling Nat. Soc. Fractals 0218-348X 9182910 http://zaguan.unizar.es/record/125872/files/texto_completo.pdf Postprint 1330206 http://zaguan.unizar.es/record/125872/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:125872 articulos driver 2024-03-18-12:58:23 ARTICLE