Fractal convolution: A new operation between functions

DOI10.1515/fca-2019-0035zbMath1426.28021arXiv1805.11316OpenAlexW2965754668WikidataQ127409291 ScholiaQ127409291MaRDI QIDQ2328628

M. A. Navascués, Peter R. Massopust

Publication date: 10 October 2019

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.11316

zbMATH Keywords

fractalsiterated function systemsfunction spacesfractal interpolation functions

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Fractals (28A80) Iteration of real functions in one variable (26A18) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27) Real-valued functions on manifolds (58C05)

Related Items

Fractal convolution on the rectangle ⋮ FRACTAL INTERPOLATION ALGORITHMS FOR COMPLEX CURVES AND SURFACES ⋮ Non-stationary \(\alpha \)-fractal functions and their dimensions in various function spaces ⋮ A very general framework for fractal interpolation functions ⋮ Fractal convolution Bessel sequences on rectangle ⋮ Convolved fractal bases and frames ⋮ Some properties of the fractal convolution of functions ⋮ Non-stationary zipper \(\alpha\)-fractal functions and associated fractal operator ⋮ Fractional vector-valued nonuniform MRA and associated wavelet packets on \(L^2\big({\mathbb{R}},{\mathbb{C}}^M\big)\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Theory of function spaces
• The capacity for a class of fractal functions
• Fractal functions and interpolation
• Accurate relationships between fractals and fractional integrals: new approaches and evaluations
• Fractal dimension of Riemann-Liouville fractional integral of 1-dimensional continuous functions
• Fundamental sets of fractal functions
• Affine fractal functions as bases of continuous functions
• FRACTAL BASES OF Lp SPACES
• Frame Perturbations
• Local Fractal Functions and Function Spaces
• Some noises withI/fspectrum, a bridge between direct current and white noise
• Fractional Brownian Motions, Fractional Noises and Applications
• An introduction to frames and Riesz bases