Fractal convolution: A new operation between functions
-
MarĂa A. NavascuĂ©s
and
Peter R. Massopust
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 đť“›p 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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© 2019 Diogenes Co., Sofia
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 22–3–2019)
- Survey Paper
- The probabilistic point of view on the generalized fractional partial differential equations
- Research Paper
- A system of coupled multi-term fractional differential equations with three-point coupled boundary conditions
- Fractal convolution: A new operation between functions
- Unique continuation principle for the one-dimensional time-fractional diffusion equation
- Asymptotics of eigenvalues for differential operators of fractional order
- The asymptotic behaviour of fractional lattice systems with variable delay
- On fractional asymptotical regularization of linear ill-posed problems in hilbert spaces
- Weighted Hölder continuity of Riemann-Liouville fractional integrals – Application to regularity of solutions to fractional cauchy problems with Carathéodory dynamics
- Green’s functions, positive solutions, and a Lyapunov inequality for a caputo fractional-derivative boundary value problem
- Finite element approximations for fractional evolution problems
- Stochastic diffusion equation with fractional Laplacian on the first quadrant
- Stability of fractional variable order difference systems
- Chaotic dynamics of fractional Vallis system for El-Niño
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 22–3–2019)
- Survey Paper
- The probabilistic point of view on the generalized fractional partial differential equations
- Research Paper
- A system of coupled multi-term fractional differential equations with three-point coupled boundary conditions
- Fractal convolution: A new operation between functions
- Unique continuation principle for the one-dimensional time-fractional diffusion equation
- Asymptotics of eigenvalues for differential operators of fractional order
- The asymptotic behaviour of fractional lattice systems with variable delay
- On fractional asymptotical regularization of linear ill-posed problems in hilbert spaces
- Weighted Hölder continuity of Riemann-Liouville fractional integrals – Application to regularity of solutions to fractional cauchy problems with Carathéodory dynamics
- Green’s functions, positive solutions, and a Lyapunov inequality for a caputo fractional-derivative boundary value problem
- Finite element approximations for fractional evolution problems
- Stochastic diffusion equation with fractional Laplacian on the first quadrant
- Stability of fractional variable order difference systems
- Chaotic dynamics of fractional Vallis system for El-Niño
