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Characterization of strongly non-linear and singular functions by scale space analysis

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  • Prodanov, Dimiter

Abstract

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.

Suggested Citation

  • Prodanov, Dimiter, 2016. "Characterization of strongly non-linear and singular functions by scale space analysis," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 14-19.
    • Handle: RePEc:eee:chsofr:v:93:y:2016:i:c:p:14-19
    DOI: 10.1016/j.chaos.2016.08.010
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
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    Cited by:

    1. Prodanov, Dimiter, 2017. "Conditions for continuity of fractional velocity and existence of fractional Taylor expansions," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 236-244.

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