A fractal operator on some standard spaces of functions
Resumen: 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 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.
Idioma: Inglés
DOI: 10.1017/S0013091516000316
Año: 2017
Publicado en: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY 60, 3 (2017), 771-776 [17 pp]
ISSN: 0013-0915

Factor impacto JCR: 0.604 (2017)
Categ. JCR: MATHEMATICS rank: 201 / 309 = 0.65 (2017) - Q3 - T2
Factor impacto SCIMAGO: 0.695 - Mathematics (miscellaneous) (Q2)

Tipo y forma: Article (PostPrint)
Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)

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 Record created 2017-10-19, last modified 2019-07-09


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