On approximation of nonlinear semi-groups

Nonlinear approximation theory on finite groups

Motivated by problems in signal recovery, we will investigate the distribution of the energy of the Fourier transform of a positive function on a finite group. In particular, we are able to bound from below the fraction of energy contained in various subsets of the Fourier transform of a positive function defined on a finite group. Applications to signal recovery for positive functions, as well...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

On Lie Semi-Groups

a subset of real Euclidean n-space, En, by (p, q) → F (p − q) = p ◦ q. In this note we shall be concerned with a representation T (.) of π as a semi-group of bounded linear operators on a Banach space X. More particularly, we suppose that postulates P1, P2, P3, P5, and P6 of chapter 25 of (2) are satisfied so that, by Theorem 25.3.1 of that book, there is a continuous function, f(.), defined on...

Deep Semi-Random Features for Nonlinear Function Approximation

We propose semi-random features for nonlinear function approximation. The flexibility of semirandom feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer models with semi-random features, we prove with no unrealistic assumptions that the model classes contain an arbitrarily good function as the width increases (univ...

Semi-groups of Operators