Searching for Sonin kernels
Manuel D. Ortigueira
Abstract
Abstract The causal shift-invariant convolution is studied from the point of view of inversion. Abel’s algorithm, used in the tautochrone problem, is considered and Sonin’s existence condition is deduced. To generate pairs of functions verifying Sonin’s condition, the class of Mittag-Leffler type functions is used. In particular, functions that are impulse responses of ARMA(N,N) systems serve as a basis. The possible use of Abel’s procedure as a support for introducing generalized fractional derivatives is evaluated.
Topics & Concepts
MathematicsConvolution (computer science)Impulse responseInversion (geology)Applied mathematicsPure mathematicsMathematical analysisArtificial intelligenceComputer scienceArtificial neural networkPaleontologyBiologyStructural basinFractional Differential Equations SolutionsControl Systems and IdentificationQuantum chaos and dynamical systems