Properties of the convolution operation in the complexity space and its dual

• José M. Hernández Morales ^[1] ; Netzahualcóyotl C. Castañeda-Roldán ^[1] ; Luz C. Álvarez-Marín ^[1]
  1. [1] Universidad Tecnológica de la Mixteca

     Universidad Tecnológica de la Mixteca

     México

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 67, Nº. 1, 2024, págs. 281-299
• Idioma: inglés
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• Resumen

  • We give the basic properties of discrete convolution in the space of complexity functions and its dual space. Two inequalities are identified, and defined in the general context of an arbitrary binary operation in any weighted quasi-metric space. In that setting, some quasi-metric and convergence consequences of those inequalities are proven. Using convolution, we show a method for building improver functionals in the complexity space. We also consider convolution in three topologies within the dual space, obtaining two topological monoids.