Some properties of the fractal convolution of functions

Navascues, M.A. (Universidad de Zaragoza) ; Mohapatra, R.N. ; Chand, A.K.B.

Resumen: We consider the fractal convolution of two maps f and g defined on a real interval as a way of generating a new function by means of a suitable iterated function system linked to a partition of the interval. Based on this binary operation, we consider the left and right partial convolutions, and study their properties. Though the operation is not commutative, the one-sided convolutions have similar (but not equal) characteristics. The operators defined by the lateral convolutions are both nonlinear, bi-Lipschitz and homeomorphic. Along with their self-compositions, they are Fre acute accent chet differentiable. They are also quasi-isometries under certain conditions of the scale factors of the iterated function system. We also prove some topological properties of the convolution of two sets of functions. In the last part of the paper, we study stability conditions of the dynamical systems associated with the one-sided convolution operators.

Idioma: Inglés

DOI: 10.1515/fca-2021-0075

Año: 2021

Publicado en: Fractional Calculus and Applied Analysis 24, 6 (2021), 1735-1757
ISSN: 1311-0454

Factor impacto JCR: 3.451 (2021)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 20 / 108 = 0.185 (2021) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 20 / 267 = 0.075 (2021) - Q1 - T1
Categ. JCR: MATHEMATICS rank: 8 / 333 = 0.024 (2021) - Q1 - T1

Factor impacto CITESCORE: 5.3 - Mathematics (Q1)

Factor impacto SCIMAGO: 1.435 - Applied Mathematics (Q1) - Analysis (Q1)

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)