Introducing the p-Laplacian Spectra
Résumé
In this work we develop a nonlinear transform, associated with nonlin-ear eigenfunctions of the p-Laplacian for p ∈ (1, 2). This bridges the gap between the Fourier transform (p = 2) and the recently proposed Total Variation (TV) transform (p = 1). We first analyze the behavior of nonlinear eigenfunctions of the p−Laplacian under the p−Laplacian flow. We provide an analytic solution and show finite extinction time. A main innovation of this study is concerned with operators of fractional homogeneity which require the mathematical framework of fractional calculus. The proposed p-Laplacian transform rigorously defines the notions of decomposition, reconstruction, filtering and spectrum. Although the study is focused on the p-Laplacian operator, the mathematical results are valid for any homogeneous operator of order in the range of (0, 1).
Origine : Fichiers produits par l'(les) auteur(s)
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