Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals

This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in infinite-dimensional Hilbert space. approach is both motivated works for total variation, where interesting results on and relation variation flow have been proven previously, recent finite-dimensional polyhedral semi-norms, gradient flows can yield into eigenvectors. We provide geometric characterization eigenvectors via dual unit ball prove them be subgradients minimal norm. connection flows, whose time evolution decomposition initial condition If these are eigenvectors, this implies orthogonality equivalence variational regularization method inverse scale space flow. Indeed we verify that all scenarios equivalences were known before other arguments - such as one-dimensional multidimensional generalizations vector fields, or certain semi-norms decompositions, further examples. also investigate extinction times profiles, which characterize very general setting, generalizing several from literature.