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FRACTAL BASES OF Lp SPACES

M. A. NAVASCUÉS

Departmento de Matemática Aplicada, Escuela de Ingeniería y Aquitectura, Centro Politécnico Superior de Ingenieros, Universidad de Zaragoza, C/María de Luna, 3, 50018 Zaragoza, Spain

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https://doi.org/10.1142/S0218348X12500132Cited by:54 (Source: Crossref)

Abstract

The methodology of fractal sets generates new procedures for the analysis of functions whose graphs have a complex geometric structure. In the present paper, a method for the definition of fractal functions is described. The new mappings are perturbed versions of classical bases as Legendre polynomials, etc. The new elements are non-differentiable and may serve as models for pseudo-random behaviour. The proposed fractal functions have good algebraic properties and good approximation properties as well. In the present paper it is proved that they constitute bases for the most important functional spaces as, for instance, the Lebesgue spaces (1 ≤ p < ∞), where I is a compact interval in the reals.

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