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Fractal Convolution: A New Operation Between Functions

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Abstract

In this paper, we define an internal binary operation between functions called fractal convolution that when applied to a pair of mappings generates a fractal function. This is done by means of a suitably defined iterated function system. We study in detail this operation in ℒp spaces and in sets of continuous functions in a way that is different from the previous work of the authors. We develop some properties of the operation and its associated sets. The lateral convolutions with the null function provide linear operators whose characteristics are explored. The last part of the article deals with the construction of convolved fractals bases and frames in Banach and Hilbert spaces of functions.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Zaragoza Calle María de Luna, 3 Zaragoza, 50018, Spain

    María A. Navascués

  2. Center of Mathematics, Research Unit M15 Technical University of Munich Boltzmannstr. 3, 85748, Garching B. Munich, Germany

    Peter R. Massopust

Authors
  1. María A. Navascués
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  2. Peter R. Massopust
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Correspondence to María A. Navascués.

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Navascués, M.A., Massopust, P.R. Fractal Convolution: A New Operation Between Functions. FCAA 22, 619–643 (2019). https://doi.org/10.1515/fca-2019-0035

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