Characterization of strongly non-linear and singular functions by scale space analysis
Copyright policy )Characterization of strongly non-linear and singular functions by scale space analysis
A central notion of physics is the rate of change. While mathematically the concept of derivative represents an idealization of the linear growth, power law types of non-linearities even in noiseless physical signals cause derivative divergence. As a way to characterize change of strongly nonlinear signals, this work introduces the concepts of scale space embedding and scale-space velocity operators. Parallels with the scale relativity theory and fractional calculus are discussed. The approach is exemplified by an application to De Rham's function. It is demonstrated how scale space embedding presents a simple way of characterizing the growth of functions defined by means of iterative function systems.
13 pages, 2 figures
- Katholieke Universiteit Leuven Belgium
Lipschitz (Hölder) classes, singular functions, fractional calculus, iteration function systems, Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives, Fractional derivatives and integrals, Mathematics - Classical Analysis and ODEs, fractals, Classical Analysis and ODEs (math.CA), FOS: Mathematics, pseudodifferential operators, Primary 26A27: Secondary 26A15, 26A33, 26A16, 47A52, 4102
Lipschitz (Hölder) classes, singular functions, fractional calculus, iteration function systems, Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives, Fractional derivatives and integrals, Mathematics - Classical Analysis and ODEs, fractals, Classical Analysis and ODEs (math.CA), FOS: Mathematics, pseudodifferential operators, Primary 26A27: Secondary 26A15, 26A33, 26A16, 47A52, 4102
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